82.17.6 problem Ex. 6

Internal problem ID [18822]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter III. Equations of the first order but not of the first degree. Problems at page 37
Problem number : Ex. 6
Date solved : Tuesday, January 28, 2025 at 12:21:36 PM
CAS classification : [[_homogeneous, `class C`], _Riccati]

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 0.132 (sec). Leaf size: 29

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

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