75.8.1 problem 199

Internal problem ID [16817]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 8. First order not solved for the derivative. Exercises page 67
Problem number : 199
Date solved : Tuesday, January 28, 2025 at 09:33:46 AM
CAS classification : [_quadrature]

\begin{align*} 4 {y^{\prime }}^{2}-9 x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.085 (sec). Leaf size: 19

dsolve(4*diff(y(x),x)^2-9*x=0,y(x), singsol=all)
 

\begin{align*} y &= -x^{{3}/{2}}+c_{1} \\ y &= x^{{3}/{2}}+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 27

DSolve[4*D[y[x],x]^2-9*x==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x^{3/2}+c_1 \\ y(x)\to x^{3/2}+c_1 \\ \end{align*}