60.1.559 problem 562

Internal problem ID [10573]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 562
Date solved : Monday, January 27, 2025 at 09:08:46 PM
CAS classification : [_dAlembert]

\begin{align*} a \left ({y^{\prime }}^{3}+1\right )^{{1}/{3}}+b x y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.366 (sec). Leaf size: 3313

dsolve(a*(diff(y(x),x)^3+1)^(1/3)+b*x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
 

\begin{align*} \text {Expression too large to display} \\ \text {Expression too large to display} \\ \text {Expression too large to display} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.090 (sec). Leaf size: 84

DSolve[-y[x] + b*x*D[y[x],x] + a*(1 + D[y[x],x]^3)^(1/3)==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\left \{x=K[1]^{\frac {b}{1-b}} \left (\frac {a \int \frac {K[1]^{\frac {2 b-1}{b-1}}}{\left (K[1]^3+1\right )^{2/3}}dK[1]}{1-b}+c_1\right ),y(x)=a \sqrt [3]{K[1]^3+1}+b x K[1]\right \},\{K[1],y(x)\}\right ] \]