82.12.6 problem Ex. 6

Internal problem ID [18771]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Examples on chapter II at page 29
Problem number : Ex. 6
Date solved : Tuesday, January 28, 2025 at 12:16:35 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 19

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

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