Question 2016.S2.30: Let y(x) be the solution of the differential equation d²y/dx......

The solution of the given differential equation is of the form

y(t)=\left(C_1+C_2 x\right) e^{2 x}

Given that y (0) = 0, so,

0=C_1

Therefore,

\begin{aligned}& y(t)=C_2 x  e^{2 x} \\& y^{\prime}(t)=C_2 e^{2 x}+2 C_2 x e^{2 x}\end{aligned}

Given that y′(0) = 1, so

Therefore,y=x e^{2 x}
Thus y(1) = e²= 7.38