Second order differential equations

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Problem: Find the solution of the Cauchy problem for the differential equation: \[ 4 y^{\prime \prime}+y=3 \cos x, \quad y(0)=-3, \quad y^{\prime}(0)=\frac{1}{2} . \] clip2net.com

8.1.2.88 Second order differential equations

1.75 $

Problem: Find the general solution of the differential equation: \[ y^{\prime \prime}+4 y^{\prime}+4 y=(2 x+3) \sin x . \] clip2net.com

8.1.2.94 Second order differential equations

1.5 $

Problem: Find the particular solution of the differential equation when \( f(x) \) is given: \[ y^{\prime \prime}+y=f(x) \text {. } \] clip2net.com

8.1.2.98 Second order differential equations

2.5 $

Problem: Solve the differential equation: \[ x^{2} y y^{\prime \prime}=\left(y-x y^{\prime}\right)^{2} \text {. } \] clip2net.com

8.1.2.1 Second order differential equations

1.75 $

Problem: Find the particular solution of the second order differential equation, satisfying the given initial conditions: \[ y^{\prime \prime}-3 y^{\prime}+2 y=2 \sin x, \quad y(0)=1, \quad y^{\prime}(0)=1 . \] clip2net.com

8.1.2.2 Second order differential equations

1.5 $

Problem: Find the general solution of the differential equation in parametric form: \[ \left(x+2 y^{\prime}\right) y^{\prime \prime}=1 \text {. } \]

8.1.2.9 Second order differential equations

1.25 $

Problem: Find the general solution of the differential equation in parametric form: \[ \left(y^{\prime \prime}\right)^{2}-2 y^{\prime} \cdot y^{\prime \prime}+3=0 . \] clip2net.com

8.1.2.11 Second order differential equations

1.75 $

Problem: Find the general solution of the differential equation in parametric form: \[ \left(2+y^{\prime}\right) e^{y^{\prime}} \cdot y^{\prime \prime}=1 . \] clip2net.com

8.1.2.13 Second order differential equations

1.25 $

Problem: Find the general solution of the differential equation in parametric form: \[ \left(3 y-2 y^{\prime}\right) y^{\prime \prime}-\left(y^{\prime}\right)^{2}=0 \text {. } \] clip2net.com

8.1.2.14 Second order differential equations

1.5 $

Problem: Find the general solution of the equation \( x y^{\prime \prime}+ \) \( +2 y^{\prime}+x y=0 \), if the function \( (\sin x) / x \) is its particular solution. clip2net.com

8.1.2.15 Second order differential equations

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Problem: Find the general solution of the equation (1\( \left.-x^{2}\right) y^{\prime \prime}-2 x y^{\prime}+2 y=0 \), if the function \( x \) is its particular solution. clip2net.com

8.1.2.16 Second order differential equations

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Problem: Solve the following equation using the method of variation of arbitrary constant: \[ y^{\prime \prime}+4 y=\frac{1}{\sin ^{2} x} \text {. } \]

8.1.2.17 Second order differential equations

1.75 $

Problem: Solve the following equation by the method of variation of arbitrary constant: \[ y^{\prime \prime}+4 y^{\prime}+4 y=e^{-2 x} \ln x \text {. } \]

8.1.2.20 Second order differential equations

1.75 $

Problem: For the given inhomogeneous differential equation \( y^{\prime \prime}+16 y=\sin (4 x+\alpha), \quad(\alpha= \) const \( ) \) write the form of its particular solution with indefinite coefficients (don't find the numerical values of the coefficients).

8.1.2.21 Second order differential equations

0.75 $

Problem: For the given inhomogeneous differential equation \( y^{\prime \prime}-4 y^{\prime}=2 \cos ^{2} 4 x \) write the form of its particular solution with indefinite coefficients (don't find the numerical values of the coefficients). clip2net.com

8.1.2.22 Second order differential equations

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