Internal problem ID [1046]
Internal file name [OUTPUT/1047_Sunday_June_05_2022_01_58_53_AM_46735432/index.tex]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number: 17.
ODE order: 1.
ODE degree: 1.
The type(s) of ODE detected by this program : "unknown"
Maple gives the following as the ode type
[[_Abel, `2nd type`, `class B`]]
Unable to solve or complete the solution.
\[ \boxed {3 x^{2} \cos \left (x \right ) y-x^{3} y^{2} \sin \left (x \right )+\left (8 y-x^{4} \sin \left (x \right ) y\right ) y^{\prime }=-4 x} \] Unable to determine ODE type.
\[ \begin {array}{lll} & {} & \textrm {Let's solve}\hspace {3pt} \\ {} & {} & 3 x^{2} \cos \left (x \right ) y-x^{3} y^{2} \sin \left (x \right )+\left (8 y-x^{4} \sin \left (x \right ) y\right ) y^{\prime }=-4 x \\ \bullet & {} & \textrm {Highest derivative means the order of the ODE is}\hspace {3pt} 1 \\ {} & {} & y^{\prime } \\ \bullet & {} & \textrm {Solve for the highest derivative}\hspace {3pt} \\ {} & {} & y^{\prime }=\frac {-3 x^{2} \cos \left (x \right ) y+x^{3} y^{2} \sin \left (x \right )-4 x}{8 y-x^{4} \sin \left (x \right ) y} \end {array} \]
✗ Solution by Maple
dsolve((3*x^2*cos(x)*y(x)-x^3*y(x)*sin(x)*y(x)+4*x)+(8*y(x)-x^4*sin(x)*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(3*x^2*Cos[x]*y[x]-x^3*y[x]*Sin[x]*y[x]+4*x)+(8*y[x]-x^4*Sin[x]*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved