First order linear differential equation

Mikesgto · 2010-12-12T03:18:51+00:00

Homework Statement 11(t+1)dy/dt-7y=28t y(0)=13 Homework Equations The Attempt at a Solution I got µ(x)=1/(t+1)^(7/11) and then used 28/11(t+1)^(7/11)*integral of t/(t+1)^(18/11) dt. And that's where I'm stuck.

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...

View full post »

Homework Statement

Homework Equations

The Attempt at a Solution

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Similar threads

Hot Threads

Prove that the integral is equal to ##\pi^2/8##

Calculating radius of gyration of plane figure about x-axis

Solve this problem that involves induction

The volume of a "spherical cap" using triple integrals

Finding the modulus and argument of ##\dfrac{a}{(b±ci)^n}##

Recent Insights

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Insights What Exactly is Dirac’s Delta Function? - Insight

Insights Relativator (Circular Slide-Rule): Simulated with Desmos - Insight

Insights Fixing Things Which Can Go Wrong With Complex Numbers

Insights Fermat's Last Theorem