Internal problem ID [11610]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises
page 37
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _exact, _rational]
\[ \boxed {\frac {1+8 x y^{\frac {2}{3}}}{x^{\frac {2}{3}} y^{\frac {1}{3}}}+\frac {\left (2 x^{\frac {4}{3}} y^{\frac {2}{3}}-x^{\frac {1}{3}}\right ) y^{\prime }}{y^{\frac {4}{3}}}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 8] \end {align*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 55
dsolve([(1+8*x*y(x)^(2/3))/(x^(2/3)*y(x)^(1/3))+((2*x^(4/3)*y(x)^(2/3)-x^(1/3))/(y(x)^(4/3)))*diff(y(x),x)=0,y(1) = 8],y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {RootOf}\left (64 \textit {\_Z}^{\frac {7}{3}} x^{4}+96 \textit {\_Z}^{\frac {5}{3}} x^{3}-729 \textit {\_Z}^{\frac {4}{3}}+48 x^{2} \textit {\_Z} +8 x \,\textit {\_Z}^{\frac {1}{3}}\right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{(1+8*x*y[x]^(2/3))/(x^(2/3)*y[x]^(1/3))+((2*x^(4/3)*y[x]^(2/3)-x^(1/3))/(y[x]^(4/3)))*y'[x]==0,{y[1]==8}},y[x],x,IncludeSingularSolutions -> True]
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