83.46.12 problem Ex 12 page 75

Internal problem ID [19577]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter V. Singular solutions
Problem number : Ex 12 page 75
Date solved : Tuesday, January 28, 2025 at 01:58:41 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} \left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (x^{2}+2 y x +y^{2}+2\right ) y^{\prime }+2 y^{2}+1&=0 \end{align*}

✗ Solution by Maple

dsolve((2*x^2+1)*diff(y(x),x)^2+(x^2+2*x*y(x)+y(x)^2+2)*diff(y(x),x)+2*y(x)^2+1=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 49

DSolve[(2*x^2+1)*D[y[x],x]^2+(x^2+2*x*y[x]+y[x]^2+2)*D[y[x],x]+2*y[x]^2+1==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {-c_1 x+1+c_1{}^2}{x+c_1} \\ y(x)\to -\frac {i}{\sqrt {2}} \\ y(x)\to \frac {i}{\sqrt {2}} \\ \end{align*}