83.22.3 problem 3

Internal problem ID [19257]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (E) at page 63
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 01:15:49 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2}&=x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.044 (sec). Leaf size: 36

dsolve(x^2*diff(y(x),x)^2-2*x*y(x)*diff(y(x),x)+2*y(x)^2=x^2,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -x \\ y \left (x \right ) &= x \\ y \left (x \right ) &= \sin \left (-\ln \left (x \right )+c_{1} \right ) x \\ y \left (x \right ) &= -\sin \left (-\ln \left (x \right )+c_{1} \right ) x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.198 (sec). Leaf size: 35

DSolve[x^2*D[y[x],x]^2-2*x*y[x]*D[y[x],x]+2*y[x]^2==x^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x \cosh (c_1-i \log (x)) \\ y(x)\to -x \cosh (i \log (x)+c_1) \\ \end{align*}