15.6.1 problem 1

Internal problem ID [2958]
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 : 1
Date solved : Monday, January 27, 2025 at 07:04:24 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+2 y&=x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 16

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

\[ y = \frac {x^{4}+4 c_{1}}{4 x^{2}} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 19

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

\[ y(x)\to \frac {x^2}{4}+\frac {c_1}{x^2} \]