Internal problem ID [8140]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 562.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_dAlembert]
\[ \boxed {a \left ({y^{\prime }}^{3}+1\right )^{\frac {1}{3}}+b x y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.297 (sec). Leaf size: 3961
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: 0.096 (sec). Leaf size: 84
DSolve[-y[x] + b*x*y'[x] + a*(1 + y'[x]^3)^(1/3)==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{x=K[1]^{\frac {b}{1-b}} \left (\frac {a \int \frac {K[1]^{\frac {2 b-1}{b-1}}}{\left (K[1]^3+1\right )^{2/3}}dK[1]}{1-b}+c_1\right ),y(x)=a \sqrt [3]{K[1]^3+1}+b x K[1]\right \},\{K[1],y(x)\}\right ] \]