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  • Show that the function is a solution of the differential equation <img alt="2\left (\frac{dy}{dx} \right )^{2}+x\left ( \frac{dy}{dx} \right

Show that the function y = ax + 2a^2 is a solution of the differential equation 2\left (\frac{dy}{dx} \right )^{2}+x\left ( \frac{dy}{dx} \right )-y=0

 

 
 
 
 
 

Answers (1)

y = ax + 2a^2

\frac{d y}{d x}=a \\

To prove:

2\left (\frac{dy}{dx} \right )^{2}+x\left ( \frac{dy}{dx} \right )-y=0 ....(i)

\mathrm{LHS} =2\left(\frac{d y}{d x}\right)^{2}+x\left(\frac{d y}{d x}\right)-y \\

Put value of \frac{d y}{d x} 

LHS=2(a)^{2}+x(a)-\left(a x+2 a^{2}\right)

LHS=0=RHS

Hence proved.

Posted by

Safeer PP

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