75.2.20 problem 40

Internal problem ID [16697]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 2. The method of isoclines. Exercises page 27
Problem number : 40
Date solved : Tuesday, January 28, 2025 at 09:18:20 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 11

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

\[ y = \frac {1}{-x +c_{1}} \]

✓ Solution by Mathematica

Time used: 0.110 (sec). Leaf size: 18

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

\begin{align*} y(x)\to -\frac {1}{x+c_1} \\ y(x)\to 0 \\ \end{align*}