82.5.5 problem Ex. 5

Internal problem ID [18741]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 20
Problem number : Ex. 5
Date solved : Tuesday, January 28, 2025 at 12:14:02 PM
CAS classification : [_exact]

\begin{align*} \left (2 x^{2} y+4 x^{3}-12 x y^{2}+3 y^{2}-x \,{\mathrm e}^{y}+{\mathrm e}^{2 x}\right ) y^{\prime }+12 x^{2} y+2 x y^{2}+4 x^{3}-4 y^{3}+2 y \,{\mathrm e}^{2 x}-{\mathrm e}^{y}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 46

dsolve((2*x^2*y(x)+4*x^3-12*x*y(x)^2+3*y(x)^2-x*exp(y(x))+exp(2*x))*diff(y(x),x)+(12*x^2*y(x)+2*x*y(x)^2+4*x^3-4*y(x)^3+2*y(x)*exp(2*x)-exp(y(x)))=0,y(x), singsol=all)
 

\[ y \left (x \right ) {\mathrm e}^{2 x}-x \,{\mathrm e}^{y \left (x \right )}+\left (-4 x +1\right ) y \left (x \right )^{3}+x^{2} y \left (x \right )^{2}+4 x^{3} y \left (x \right )+x^{4}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.336 (sec). Leaf size: 51

DSolve[(2*x^2*y[x]+4*x^3-12*x*y[x]^2+3*y[x]^2-x*Exp[y[x]]+Exp[2*x])*D[y[x],x]+(12*x^2*y[x]+2*x*y[x]^2+4*x^3-4*y[x]^3+2*y[x]*Exp[2*x]-Exp[y[x]])==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x^4+4 x^3 y(x)+x^2 y(x)^2-x e^{y(x)}-4 x y(x)^3+y(x)^3+e^{2 x} y(x)=c_1,y(x)\right ] \]