44.1.53 problem 64

Internal problem ID [6928]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 64
Date solved : Monday, January 27, 2025 at 02:37:10 PM
CAS classification : [_quadrature]

\begin{align*} x {y^{\prime }}^{2}-4 y^{\prime }-12 x^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 49

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

\begin{align*} y &= -2 \left (\int \frac {-1+\sqrt {3 x^{4}+1}}{x}d x \right )+c_{1} \\ y &= 2 \left (\int \frac {1+\sqrt {3 x^{4}+1}}{x}d x \right )+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 67

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

\begin{align*} y(x)\to \sqrt {3 x^4+1}+\log \left (\sqrt {3 x^4+1}-1\right )+c_1 \\ y(x)\to -\sqrt {3 x^4+1}+\log \left (\sqrt {3 x^4+1}+1\right )+c_1 \\ \end{align*}