Internal problem ID [10132]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 13. Linear
equations of first order. Page 19
Problem number: Ex 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (x^{3}+x \right ) y^{\prime }+4 x^{2} y-2=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve((x+x^3)*diff(y(x),x)+4*x^2*y(x)=2,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2}+2 \ln \relax (x )+c_{1}}{\left (x^{2}+1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 23
DSolve[(x+x^3)*y'[x]+4*x^2*y[x]==2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2+2 \log (x)+c_1}{\left (x^2+1\right )^2} \\ \end{align*}