15.6.10 problem 10

Internal problem ID [2967]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 10, page 41
Problem number : 10
Date solved : Monday, January 27, 2025 at 07:04:46 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 19

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

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