73.2.4 problem 3.4 d

Internal problem ID [15027]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 3. Some basics about First order equations. Additional exercises. page 63
Problem number : 3.4 d
Date solved : Tuesday, January 28, 2025 at 07:27:52 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 9

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

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

✓ Solution by Mathematica

Time used: 0.543 (sec). Leaf size: 45

DSolve[x^2*D[y[x],x]+x*y[x]^2==x,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 ][-\log (x)+c_1] \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}