77.1.67 problem 87 (page 123)

Internal problem ID [17957]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 87 (page 123)
Date solved : Tuesday, January 28, 2025 at 11:18:19 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

dsolve(diff(y(x),x)=sqrt(y(x)),y(x), singsol=all)
 

\[ \sqrt {y}-\frac {x}{2}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.098 (sec). Leaf size: 20

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

\begin{align*} y(x)\to \frac {1}{4} (x+c_1){}^2 \\ y(x)\to 0 \\ \end{align*}