40.3.19 problem 25 (d)

Internal problem ID [6623]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 25 (d)
Date solved : Monday, January 27, 2025 at 02:16:15 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

\begin{align*} -y-3 x^{2} \left (x^{2}+y^{2}\right )+x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 14

dsolve((-y(x)-3*x^2*(x^2+y(x)^2))+x*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \tan \left (x^{3}+3 c_1 \right ) x \]

✓ Solution by Mathematica

Time used: 0.240 (sec). Leaf size: 14

DSolve[(-y[x]-3*x^2*(x^2+y[x]^2))+x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \tan \left (x^3+c_1\right ) \]