Generating...                               quiz02_n9

  1. Solve the exact ODE $\displaystyle 2\,x^2\,y\,\left({{d}\over{d\,x}}\,y\right)+2\,x\,y^2=0$.

    $\displaystyle x^2\,y^2+2\,y+2\,x=c$ $\displaystyle x^2\,y^2+2\,y=c$ $\displaystyle x^2\,y^2+2\,x=c$ $\displaystyle x^2\,y^2=c$

  2. Solve the homogeneous ODE $\displaystyle x\,\left({{d}\over{d\,x}}\,y\right)-y+x=0$.

    $\displaystyle y={{x}\over{2}}+{{c}\over{x}}$ $\displaystyle y=x\,\ln x+c\,x$ $\displaystyle y=c\,x-x\,\ln x$ $\displaystyle y={{c}\over{x}}-{{x}\over{2}}$

  3. Find the value of k so that the ODE $\displaystyle \left(-2\,x\,e^{2\,y}-8\,x\,y^3\right)\,\left({{d}\over{d\,x}}\,y \right)-e^{2\,y}+k\,y^4+2\,x=0$ becomes exact.

    k = −1 k = 1 k = −2 k = 2

  4. Solve the exact ODE $\displaystyle -\sin x\,\sin y\,\left({{d}\over{d\,x}}\,y\right)+\cos x\,\cos y+ \tan x=0$.

    $\displaystyle \sin x\,\cos y+\ln \csc x=c$ $\displaystyle \sin x\,\cos y+\ln \sec x=c$ $\displaystyle \cos x\,\sin y+\ln \csc x=c$ $\displaystyle \cos x\,\sin y+\ln \sec x=c$

  5. Solve the exact ODE $\displaystyle \left(x+1\right)\,\left({{d}\over{d\,x}}\,y\right)+y+1=0$ subject to the initial condition y(1) = 2

    xy + y + x = 5 xy + x = 2 xy + y = 4 xy = 1


Department of Mathematics
Last modified: 2026-07-16