Internal problem ID [1713]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.1, second order linear differential equations. Page 134
Problem number: 5(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 2, y^{\prime }\relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.017 (sec). Leaf size: 9
dsolve([2*t^2*diff(y(t),t$2)+3*t*diff(y(t),t)-y(t)=0,y(1) = 2, D(y)(1) = 1],y(t), singsol=all)
\[ y \relax (t ) = 2 \sqrt {t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 12
DSolve[{2*t^2*y''[t]+3*t*y'[t]-y[t]==0,{y[1]==2,y'[1]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 2 \sqrt {t} \\ \end{align*}