What is Ivp: Definition and 144 Discussions

InterVarsity Press (IVP) was founded in 1947 by InterVarsity Christian Fellowship/USA as a publisher of evangelical Christian books. It is headquartered in Downers Grove, Illinois.

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1. Solving An IVP on Matlab with ODE 45 with different tolerances

My code is as follows: but when I use the function in my command window exactsol(t) and input a tolerance but there is an error in LINE 19 saying unrecognized ivpfun, could someone help me fix it as I am unsure of how to proceed from here. function y = exactsol(t) y = zeros (2,1); y(1) =...
2. MHB Find the solution y to the IVP

$y'=y+2te^{2t}$
3. MHB B.2.2.16 IVP of \dfrac{x(x^2+1)}{4y^3}, y(0)=-\dfrac{1}{\sqrt{2}}

Find the solution of $y^{\prime} = \dfrac{x(x^2+1)}{4y^3}, \quad y(0)=-\dfrac{1}{\sqrt{2}}$ in explicit form. rewrite $\dfrac{y}{x}=\dfrac{x(x^2+1)}{4y^3}= y^3\, dy=\dfrac{x(x^2+1)}{4}\, dx$ integrate $\dfrac{y^4}{4}= \dfrac{1}{4}\left(\dfrac{x^4}{4} +\dfrac{ x^2}{2}\right)$...
4. MHB What is the integrating factor for solving this IVP?

find the solution of the IVP $ty'+2y=t^2-t+1, \quad y(1)=\dfrac{1}{2}, \quad t>0$\begin{array}{lll} \textsf{Divide thru by t} & y'+\dfrac{2}{t}y=t-1+\dfrac{1}{t}\\ \textsf{Find u(t)} &u(t)=\exp\displaystyle\int \dfrac{2}{t} \, dx =e^{2ln |t|}+c \end{array} so far anyway... is...
5. MHB Solving IVP $y''-y=0$ with $y_1,y_2$

$\tiny{b.1.3.7}$ Solve IVP $y''-y=0;\quad y_1(t)=e^t,\quad y_2(t)=\cosh{t}$ $\begin{array}{lll} &\exp\left(\int \, dx\right)= e^x\\ & e^x(y''-y)=0\\ & e^x-e^x=0\\ \\ &y_1(x)=e^x\\ &(e^x)''-(e^x)=0\\ &(e^x)-(e^x)=0\\ \\ &y_2(x)=\cosh{x}\\ &(\cosh{x})''-(\cosh{x})=0\\ \end{array}$ ok there was...

20. MHB Solve IVP 2000 #23: Y(0)=A Solution

2000 given #23 so far I could not get to the W|A solution before applying the y(0)=ahere is the book answer for the rest
21. MHB -2.2.20 IVP interval....trig subst y^2(1-x^2)^{1/2} \,dy=\arcsin{x}\,dx

(a) find solution of initial value and (c) interval $$\quad\displaystyle y^2(1-x^2)^{1/2} \,dy = \arcsin{x}\,dx, \quad y(0) = 1$$ separate $$y^2 \,dy = \frac{\arcsin{x}}{(1-x^2)^{1/2}}\,dx,$$ Integrate \begin{align*} \int y^2 \,dy& = \int\frac{\arcsin{x}}{\sqrt{(1-x^2)}}\,dx...

41. MHB Verify My IVP Help Appreciated!

Need someone to verify that my solution is correct, thanks in advance. Solve the IVP $y'' - y = e^t$, $y(0) = 0$, $y'(0) = 1$ Solution: $\frac{1}{2}te^t + \frac{1}{2}e^t - \frac{1}{2}e^{-t}$
42. What's the General Solution to This IVP?

\frac {dy}{dt} = y^3 + t^2, y(0) = 0 My teacher said this IVP couldn't be expressed in terms of functions we commonly know. I was wondering what the general solution is? Thank-you
43. MHB Find the unique solution to the IVP

Find the unique solution to the IVP $t^3y'' + e^ty' + t^4y = 0$ $y(1) = 0$ , $y'(1) = 0$ Should I start out by dividing through by $t^4$ to get $\frac{1}{t} y" + \frac{e^t}{t^4}y' + y = 0$
44. MHB Solving the IVP, leaving it in Implicit Form

Solve the IVP. $(2x-y)dx + (2y-x)dy = 0$. $y(1) = 3$. Leave solution in implicit form. So I got: $\frac{dy}{dx} = \frac{-(2x-y)}{2y-x}$ Would this be correct since I didn't explicitly solve for $dy$ ?
45. MHB Finding the explicit solution to the IVP

Find the explicit solution to the IVP. $xdx + ye^{-x}dy=0$, $y(0) =1$ so I did some manipulation to get $ye^{-x}dy= -xdx$ ==> $\frac{dy}{dx}=\frac{-x}{ye^{-x}}$ but now I'm confused on what to do. What I found above is the implicit solution right? So do I just need to get $y'$ on the left side...
46. Solving IVPs with Unstable Functions

Homework Statement http://s14.postimg.org/an6f4t2ht/Untitled.png Homework EquationsThe Attempt at a Solution I'm not sure what they want me to do on the last part. I tried some googling and looking in my textbooks but I didn't find any examples. It seems to me like the function goes to...
47. Find the constants for given IVP

Homework Statement Homework Equations DifEqs The Attempt at a Solution y ' = 4C1e-4xSinX - 4C2e-4xCosX y'(0) = -1 -1 = 0 - 4C2 Therefore C2 = 1/4 Not correct. What am I doing wrong?
48. Laplace Transform for Solving a First Order Linear IVP

Homework Statement Solve the IVP : dy/dt + y = f(t) y(0) = -5 where f(t) = -1, 0 <= t < 7 -5, t >= 7 y(t) for 0 <= t < 7 = ? y(t) for t >= 7 = ? Homework EquationsThe Attempt at a Solution So I have never seen a problem of this type, excuse my silly mistakes if I'm interpreting this question...
49. MHB Find specific solution to IVP with two parameters

x=c_1 cos(t)+c_2sin(t) is a family of solution to x''+x=0. Given x(\frac{\pi}{6})=\frac{1}{2} and x'(\frac{\pi}{6})=0 find a solution to the second order IVP consisting of this differential equation and the given intial conditions. The answer key has x=\frac{\sqrt{3}}{4}cos(t)+\frac{1}{4}sin(t)...
50. Problems with uniqueness of IVP

Are these statements correct, if not could you give me an example 1. If solution of IVP is non-unique then there are infinitely many solutions in short, if the solution to the IVP has at least 2 solutions then there are infinitely many solutions to this IVP 2.there are none IVP first...