6.5 problem Ex 5

Internal problem ID [10133]

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 5.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {x^{2} y^{\prime }+\left (-2 x +1\right ) y-x^{2}=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 17

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

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

Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 19

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

\begin{align*} y(x)\to x^2 \left (1+c_1 e^{\frac {1}{x}}\right ) \\ \end{align*}