73.7.26 problem 26

Internal problem ID [15184]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 26
Date solved : Tuesday, January 28, 2025 at 07:40:38 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=x y^{2}+3 y^{2}+x +3 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 15

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

\[ y = \tan \left (\frac {1}{2} x^{2}+c_{1} +3 x \right ) \]

✓ Solution by Mathematica

Time used: 0.262 (sec). Leaf size: 36

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

\[ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1]^2+1}dK[1]\&\right ]\left [\frac {x^2}{2}+3 x+c_1\right ] \]