82.48.6 problem Ex. 6

Internal problem ID [18987]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. End of chapter problems at page 107
Problem number : Ex. 6
Date solved : Tuesday, January 28, 2025 at 12:43:53 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} {y^{\prime }}^{2}-y y^{\prime \prime }&=n \sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.394 (sec). Leaf size: 101

dsolve(diff(y(x),x)^2-y(x)*diff(y(x),x$2)=n*sqrt(diff(y(x),x)^2+a^2*diff(y(x),x$2)^2),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= c_{1} \\ y \left (x \right ) &= \frac {a n \left ({\mathrm e}^{\frac {\sqrt {c_{1}^{2}-n^{2}}\, \left (c_{2} +x \right )}{a n}}-c_{1} \right )}{\sqrt {c_{1}^{2}-n^{2}}} \\ y \left (x \right ) &= c_{1} x +c_{2} \\ y \left (x \right ) &= c_{1} {\mathrm e}^{\frac {x}{a}}+c_{2} {\mathrm e}^{-\frac {x}{a}} \\ y \left (x \right ) &= c_{1} \sin \left (\frac {x}{a}\right )+c_{2} \cos \left (\frac {x}{a}\right ) \\ \end{align*}

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[D[y[x],x]^2-y[x]*D[y[x],{x,2}]==n*Sqrt[D[y[x],x]^2+a^2*D[y[x],{x,2}]^2],y[x],x,IncludeSingularSolutions -> True]
 

Not solved