15.5.19 problem 23

Internal problem ID [2955]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 9, page 38
Problem number : 23
Date solved : Monday, January 27, 2025 at 07:00:32 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✗ Solution by Maple

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

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.204 (sec). Leaf size: 29

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

\[ \text {Solve}\left [x^2 \left (-e^{-y(x)}\right )-e^{-y(x)} y(x)^2=-1,y(x)\right ] \]