62.9.6 problem Ex 6

Internal problem ID [12837]
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 16. Integrating factors by inspection. Page 23
Problem number : Ex 6
Date solved : Tuesday, January 28, 2025 at 04:26:18 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 10

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

\[ y = \tan \left (x +c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.091 (sec). Leaf size: 28

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{K[1]^2+1}dK[1]=x+c_1,y(x)\right ] \]