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ODE Second Order ODE Worksheets - Download free PDFs

ODE

Second Order ODE

Real Roots

1.\:\:y^{\prime\prime}-y^{\prime}-y=0

2.\:\:\frac{d^{2}x}{dt^{2}}-64x=0

3.\:\:2y^{\prime\prime}+y^{\prime}=y

4.\:\:y^{\prime\prime}-y^{\prime}-2y=0

5.\:\:3y^{\prime\prime}-10y^{\prime}+2y=0

6.\:\:y^{\prime\prime}-4y=0

7.\:\:2y^{\prime\prime}+3y^{\prime}-2y=0

8.\:\:y^{\prime\prime}+7y^{\prime}-30y=0

9.\:\:\frac{d^{2}}{dx^{2}}y+3\frac{d}{dx}y+2y=0

10.\:\:y^{\prime\prime}+y^{\prime}=y

ODE

Second Order ODE

Complex Roots

1.\:\:y^{\prime\prime}+2y^{\prime}+2y=0

2.\:\:y^{\prime\prime}+y=0

3.\:\:y^{\prime\prime}-4y^{\prime}+13y=0

4.\:\:4y^{\prime\prime}+4y^{\prime}+5y=0

5.\:\:y^{\prime\prime}+y^{\prime}+y=0

6.\:\:y^{\prime\prime}+6y^{\prime}+13y=0,\:y(0)=0

7.\:\:y^{\prime\prime}=-2y

8.\:\:9y^{\prime\prime}=-25y

9.\:\:y^{\prime\prime}=-2y,\:y(π)=\frac{1}{2}

10.\:\:y^{\prime\prime}+6y^{\prime}+25y=0

ODE

Second Order ODE

One Root

1.\:\:0.25y^{\prime\prime}-2y^{\prime}+4y=0

2.\:\:16y^{\prime\prime}-8y^{\prime}+y=0,\:y(0)=40

3.\:\:y^{\prime\prime}=0

4.\:\:9\frac{d^{2}y}{dx^{2}}-6\frac{dy}{dx}+y=0

5.\:\:y^{\prime\prime}+2y^{\prime}+y=0

6.\:\:y^{\prime\prime}+14y^{\prime}+49y=0

7.\:\:100y^{\prime\prime}+60y^{\prime}+9y=0

8.\:\:100y^{\prime\prime}+60y^{\prime}+9y=0,\:y(1)=8

9.\:\:y^{\prime\prime}-6y^{\prime}+9y=0

10.\:\:4y^{\prime\prime}+12y^{\prime}+9y=0

ODE

Second Order ODE

Non-Homogeneous

1.\:\:y^{\prime\prime}-y^{\prime}-2y=-2t+4t^{2}

2.\:\:y^{\prime\prime}-4y^{\prime}+3y=2\cos(x)+4\sin(x)

3.\:\:y^{\prime\prime}-2y^{\prime}+y=2\sin(t)

4.\:\:y^{\prime\prime}+3y=30e^{2t}

5.\:\:y^{\prime\prime}-18y^{\prime}+141y=9e^{3t}

6.\:\:y^{\prime\prime}-y^{\prime}=-\cos(x)

7.\:\:y^{\prime\prime}+3y^{\prime}+2y=t^{2}

8.\:\:y^{\prime\prime}+3y^{\prime}+5y=2e^{-3x}

9.\:\:y^{\prime\prime}+y^{\prime}-2y=36e^{2t}

10.\:\:\frac{1}{4}y^{\prime\prime}+y^{\prime}+y=x^{2}-2x