62.11.1 problem Ex 1

Internal problem ID [12843]
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 18. Transformation of variables. Page 26
Problem number : Ex 1
Date solved : Tuesday, January 28, 2025 at 04:26:43 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }-y+2 x^{2} y-x^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(x*diff(y(x),x)-y(x)+2*x^2*y(x)-x^3=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 21

DSolve[x*D[y[x],x]-y[x]+2*x^2*y[x]-x^3==0,y[x],x,IncludeSingularSolutions -> True]
 

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