Internal problem ID [7652]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 71.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]]
Solve \begin {gather*} \boxed {y^{\prime }-\sqrt {\frac {b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}{a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 113
dsolve(diff(y(x),x) - sqrt((b__4*y(x)^4+b__3*y(x)^3+b__2*y(x)^2+b__1*y(x)+b__0)/(a__4*x^4+a__3*x^3+a__2*x^2+a__1*x+a__0))=0,y(x), singsol=all)
\[ \int _{}^{y \relax (x )}\frac {1}{\sqrt {\textit {\_a}^{4} b_{4}+\textit {\_a}^{3} b_{3}+\textit {\_a}^{2} b_{2}+\textit {\_a} b_{1}+b_{0}}}d \textit {\_a} +\int _{}^{x}-\frac {\sqrt {\frac {b_{4} y \relax (x )^{4}+b_{3} y \relax (x )^{3}+b_{2} y \relax (x )^{2}+b_{1} y \relax (x )+b_{0}}{\textit {\_a}^{4} a_{4}+\textit {\_a}^{3} a_{3}+\textit {\_a}^{2} a_{2}+\textit {\_a} a_{1}+a_{0}}}}{\sqrt {b_{4} y \relax (x )^{4}+b_{3} y \relax (x )^{3}+b_{2} y \relax (x )^{2}+b_{1} y \relax (x )+b_{0}}}d \textit {\_a} +c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 22.243 (sec). Leaf size: 2237
DSolve[y'[x] - Sqrt[(b4*y[x]^4+b3*y[x]^3+b2*y[x]^2+b1*y[x]+b0)/(a4*x^4+a3*x^3+a2*x^2+a1*x+a0)]==0,y[x],x,IncludeSingularSolutions -> True]
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