62.32.8 problem Ex 8

Internal problem ID [12985]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VIII, Linear differential equations of the second order. Article 55. Summary. Page 129
Problem number : Ex 8
Date solved : Tuesday, January 28, 2025 at 04:46:21 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+2 \left (1+x \right ) y&=x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 19

dsolve(x^2*diff(y(x),x$2)-2*x*(1+x)*diff(y(x),x)+2*(1+x)*y(x)=x^3,y(x), singsol=all)
 

\[ y = -\frac {x \left (-2 \,{\mathrm e}^{2 x} c_{1} -2 c_{2} +x \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.079 (sec). Leaf size: 31

DSolve[x^2*D[y[x],{x,2}]-2*x*(1+x)*D[y[x],x]+2*(1+x)*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{4} x \left (2 x-2 c_2 e^{2 x+1}+1-4 e c_1\right ) \]