69.1.54 problem 73

Internal problem ID [14207]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 73
Date solved : Tuesday, January 28, 2025 at 06:21:56 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 47

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

\begin{align*} y &= \frac {x}{4}-\frac {\sqrt {-8 x^{3}+x^{2}+8 c_{1}}}{4} \\ y &= \frac {x}{4}+\frac {\sqrt {-8 x^{3}+x^{2}+8 c_{1}}}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.133 (sec). Leaf size: 67

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

\begin{align*} y(x)\to \frac {1}{4} \left (x-i \sqrt {8 x^3-x^2-16 c_1}\right ) \\ y(x)\to \frac {1}{4} \left (x+i \sqrt {8 x^3-x^2-16 c_1}\right ) \\ \end{align*}