73.3.39 problem 4.7 (m)

Internal problem ID [15073]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.7 (m)
Date solved : Tuesday, January 28, 2025 at 07:29:42 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 14

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

\[ y = -\tanh \left (x^{3}+3 c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.318 (sec). Leaf size: 44

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

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