77.1.96 problem 123 (page 179)

Internal problem ID [17986]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 123 (page 179)
Date solved : Tuesday, January 28, 2025 at 11:19:28 AM
CAS classification : [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

\begin{align*} a^{2} y^{\prime \prime }&=2 x \sqrt {{y^{\prime }}^{2}+1} \end{align*}

✗ Solution by Maple

dsolve(a^2*diff(y(x),x$2)=2*x*sqrt(1+diff(y(x),x)^2),y(x), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.481 (sec). Leaf size: 50

DSolve[a^2*D[y[x],{x,2}]==2*x*Sqrt[1+D[y[x],x]^2],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2-\frac {1}{4} \sqrt {\pi } a \left (\text {erf}\left (\frac {x}{a}\right ) (\cosh (c_1)-\sinh (c_1))-\text {erfi}\left (\frac {x}{a}\right ) (\cosh (c_1)+\sinh (c_1))\right ) \]