75.13.5 problem 322

Internal problem ID [16910]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 13. Basic concepts and definitions. Exercises page 98
Problem number : 322
Date solved : Tuesday, January 28, 2025 at 09:40:38 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{4}&=1 \end{align*}

✓ Solution by Maple

Time used: 0.098 (sec). Leaf size: 31

dsolve(diff(y(x),x)*diff(y(x),x)^3=1,y(x), singsol=all)
 

\begin{align*} y &= -i x +c_{1} \\ y &= i x +c_{1} \\ y &= -x +c_{1} \\ y &= x +c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 43

DSolve[D[y[x],x]*D[y[x],x]^3==1,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x+c_1 \\ y(x)\to c_1-i x \\ y(x)\to i x+c_1 \\ y(x)\to x+c_1 \\ \end{align*}