80.7.1 problem 1 (eq 98)

Internal problem ID [18579]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter V. Singular solutions. section 36. Problems at page 99
Problem number : 1 (eq 98)
Date solved : Tuesday, January 28, 2025 at 12:00:58 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} 4 y {y^{\prime }}^{3}-2 x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }+x^{3}&=16 y^{2} \end{align*}

✗ Solution by Maple

dsolve(4*y(x)*diff(y(x),x)^3-2*x^2*diff(y(x),x)^2+4*x*y(x)*diff(y(x),x)+x^3=16*y(x)^2,y(x), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 50.040 (sec). Leaf size: 49162

DSolve[4*y[x]*D[y[x],x]^3-2*x^2*D[y[x],x]^2+4*x*y[x]*D[y[x],x]+x^3==16*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

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