Recent content by nufeng

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    Undergrad Covert differential equation into a system of 1st order ODE?

    solve by MAPLE first, solve 2nd order differential equation ode2 := x^2*(diff(f(x), x, x))-2*x*(diff(f(x), x))+2*f(x) = 0 ics2 := (D(f))(1) = 9, f(1) = 4 dsolve([ode2, ics2]) answer is f(x) = 5*x^2-x convert to a system of 1st ode sys1ode := diff(y(t), t) = z(t), diff(z(t), t) =...
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    Undergrad Covert differential equation into a system of 1st order ODE?

    Thank you! I know how to do it.
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    Undergrad Covert differential equation into a system of 1st order ODE?

    How to covert this differential equation into a system of one order ODE? (require covert the equation into a system of 1st-order equations and solve by using ode23 in matlab) x^2*y''-2*x*y'+2*y = 0; y(1) = 4; y'(1)=0; solve for y(x) I tried to convert it get X' = AX in which X...
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    Graduate How to covert this differential equation into a system of one order ODE?

    How to covert this differential equation into a system of one order ODE? x^2*y''-2*x*y'+2*y = 0; y(1) = 4; y'(1)=0; solve for y(x) I tried to convert it get X' = AX in which X = [y, z]' A = [0, 1; 2/x^2, 2/x]; But x exists in A, which cannot solve by dsolve in Matlab.
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    Undergrad Question about solving ODE with Complex eigenvalue

    AlephZero, thank you! Really helpful!
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    Undergrad Question about solving ODE with Complex eigenvalue

    For example, ODE: y'' + y = 0 solve this problem using MAPLE f(x) = _C1*sin(x)+_C2*cos(x) My question is Eigenvalue for D^2+1=0 is +i, -i so general solution is f(x) = C1*exp(i*x)+C2*exp(-i*x) according to Euler's formula f(x) = C1( cos(x)+i*sin(x) ) + C2*( cos(x)-i*sin(x) ) it is different...