Help me prove differential equation

zabcima
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please help me find the answer..

1. Prove that lny=C_1e^x+ C_2e^-x is the solution of differential equation
yy''-(y')^2 =y^2lny note:(C_1)meaning C sub 1, a constant value


2. y^-3=x^3(3e^x+c) is the solution of differential equation xy'+y+x^4y^4e^x=0
note: a while ago i forgot to emphasize that the value of y'' is that it is a double prime.
pls.! help me prove it.thanks
 
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zabcima said:
please help me find the answer..

1. Prove that lny=C_1e^x+ C_2e^-x is the solution of differential equation
yy''-(y')^2 =y^2lny note:(C_1)meaning C sub 1, a constant value


2. y^-3=x^3(3e^x+c) is the solution of differential equation xy'+y+x^4y^4e^x=0
note: a while ago i forgot to emphasize that the value of y'' is that it is a double prime.
pls.! help me prove it.thanks
Welcome to Physics Forums.

We are more than happy to help you, but you must show some effort in attempting to solve the problems yourself.

HINT: The solution of a differential equation, by definition, satisfies the differential equation.
 

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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