62.6.4 problem Ex 4

Internal problem ID [12822]
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
Date solved : Tuesday, January 28, 2025 at 04:24:51 AM
CAS classification : [_linear]

\begin{align*} \left (x^{3}+x \right ) y^{\prime }+4 x^{2} y&=2 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

dsolve((x+x^3)*diff(y(x),x)+4*x^2*y(x)=2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 23

DSolve[(x+x^3)*D[y[x],x]+4*x^2*y[x]==2,y[x],x,IncludeSingularSolutions -> True]
 

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