Internal problem ID [7582]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {1}{\sqrt {\mathit {a4} \,x^{4}+\mathit {a3} \,x^{3}+\mathit {a2} \,x^{2}+\mathit {a1} x +\mathit {a0}}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 30
dsolve(diff(y(x),x) - (a4*x^4+a3*x^3+a2*x^2+a1*x+a0)^(-1/2)=0,y(x), singsol=all)
\[ y \relax (x ) = \int \frac {1}{\sqrt {\mathit {a4} \,x^{4}+\mathit {a3} \,x^{3}+\mathit {a2} \,x^{2}+\mathit {a1} x +\mathit {a0}}}d x +c_{1} \]
✓ Solution by Mathematica
Time used: 10.29 (sec). Leaf size: 1030
DSolve[y'[x] - (a4*x^4+a3*x^3+a2*x^2+a1*x+a0)^(-1/2)==0,y[x],x,IncludeSingularSolutions -> True]
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