48.4.20 problem Problem 3.33

Internal problem ID [7562]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.6 Summary and Problems. Page 218
Problem number : Problem 3.33
Date solved : Monday, January 27, 2025 at 03:06:09 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.006 (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: 0.241 (sec). Leaf size: 12

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

\[ y(x)\to x \tan (x+c_1) \]