How Can I Solve This Differential Equation?

John999
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I'm having problems solving this differential equation:

x*dy/dx-2*y=(x^2)*cos(x)

y(pi/2)=0

Thanks
 
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John999 said:
I'm having problems solving this differential equation:

x*dy/dx-2*y=(x^2)*cos(x)

y(pi/2)=0

Thanks
Can one think of a way that xy'-2y looks like the derivative of a quotient?
 
John999 said:
I'm having problems solving this differential equation:

x*dy/dx-2*y=(x^2)*cos(x)

y(pi/2)=0

Thanks


you can always divide by x and then you know...integrating factor it
 

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...
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