59.1.200 problem 202

Internal problem ID [9372]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 202
Date solved : Monday, January 27, 2025 at 06:02:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 1.993 (sec). Leaf size: 60

dsolve(diff(y(t),t$2)+(t^2+2*t+1)*diff(y(t),t)-(4+4*t)*y(t)=0,y(t), singsol=all)
 

\[ y = \left (t +1\right ) \left (t^{3}+3 t^{2}+3 t +5\right ) \left (c_{2} \left (\int \frac {{\mathrm e}^{-\frac {t \left (t^{2}+3 t +3\right )}{3}}}{\left (t +1\right )^{2} \left (t^{3}+3 t^{2}+3 t +5\right )^{2}}d t \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 4.118 (sec). Leaf size: 78

DSolve[D[y[t],{t,2}]+(t^2+2*t+1)*D[y[t],t]-(4+4*t)*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to (t+1) \left (t^3+3 t^2+3 t+5\right ) \left (c_2 \int _1^t\frac {e^{-\frac {1}{3} K[1] \left (K[1]^2+3 K[1]+3\right )}}{(K[1]+1)^2 \left (K[1]^3+3 K[1]^2+3 K[1]+5\right )^2}dK[1]+c_1\right ) \]