62.6.5 problem Ex 5

Internal problem ID [12823]
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
Date solved : Tuesday, January 28, 2025 at 04:24:53 AM
CAS classification : [_linear]

\begin{align*} x^{2} y^{\prime }+\left (1-2 x \right ) y&=x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 21

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

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