29.9.12 problem 252

Internal problem ID [4852]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 252
Date solved : Monday, January 27, 2025 at 09:42:44 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 21

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

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