60.1.1 problem 1

Internal problem ID [10015]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 1
Date solved : Monday, January 27, 2025 at 06:18:16 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-\frac {1}{\sqrt {\operatorname {a4} \,x^{4}+\operatorname {a3} \,x^{3}+\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0}}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (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)
 

\[ y = \int \frac {1}{\sqrt {\operatorname {a4} \,x^{4}+\operatorname {a3} \,x^{3}+\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0}}}d x +c_{1} \]

✓ Solution by Mathematica

Time used: 10.288 (sec). Leaf size: 1117

DSolve[D[y[x],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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