62.14.4 problem Ex 4

Internal problem ID [12885]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IV, differential equations of the first order and higher degree than the first. Article 25. Equations solvable for \(y\). Page 52
Problem number : Ex 4
Date solved : Tuesday, January 28, 2025 at 04:31:50 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

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

✓ Solution by Maple

Time used: 0.071 (sec). Leaf size: 31

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

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

✓ Solution by Mathematica

Time used: 0.140 (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*}