Generating...                               quiz03_n14

  1. Solve the linear ODE $\displaystyle x^2\,\left({{d}\over{d\,x}}\,y\right)-2\,x\,\left({{d}\over{d\,x}} \,y\right)+2\,y=0$ subject to the initial condition y(3) = 6

    $\displaystyle y={{x^3}\over{2\,x-4}}-{{3\,x}\over{2\,x-4}}$ $\displaystyle y={{x^3}\over{2\,x-4}}-{{5\,x}\over{2\,x-4}}$ $\displaystyle y={{2\,x}\over{x-2}}$ $\displaystyle y={{3\,x}\over{x-2}}$

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

    $\displaystyle y={{c}\over{e^{x}-1}}$ $\displaystyle y={{c}\over{e^{x}-1}}-{{x^2}\over{2\,e^{x}-2}}$ $\displaystyle y={{c}\over{e^{x}+1}}$ $\displaystyle y={{x^2}\over{2\,e^{x}+2}}+{{c}\over{e^{x}+1}}$

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

    $\displaystyle y={{x\,\ln x}\over{x+1}}-{{x}\over{x+1}}+{{5}\over{x+1}}$ $\displaystyle y={{x\,\ln x}\over{x+1}}-{{x}\over{x+1}}+{{3}\over{x+1}}$ $\displaystyle y={{4}\over{x+1}}$ $\displaystyle y={{2}\over{x+1}}$

  4. Solve the linear ODE $\displaystyle y\,\sec z\,\tan z+{{d}\over{d\,z}}\,y\,\sec z-\cos z=0$.

    $\displaystyle y=\sin ^2z+c\,\sin z$ $\displaystyle y=c\,\sin z-\cos z\,\sin z$ $\displaystyle y={{\sin z}\over{\sec z}}+{{c}\over{\sec z}}$ $\displaystyle y={{c}\over{\sec z}}-{{\cos z}\over{\sec z}}$

  5. Solve the linear ODE $\displaystyle {{d}\over{d\,x}}\,y+x^2\,y-2\,x^2=0$.

    $\displaystyle y=c\,e^ {- x }+2\,x^2-4\,x+4$ $\displaystyle y=c\,e^ {- {{x^3}\over{3}} }+2$ $\displaystyle y=c\,e^ {- x }+x^2-2\,x+2$ $\displaystyle y=c\,e^ {- {{x^3}\over{3}} }+1$


Department of Mathematics
Last modified: 2025-05-04