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Differential equations
Solve the differential equations
The answer is always a linear combination of all possible linearly independent solutions (with initial values)
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Last updated: March 12, 2025
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| First submitted | March 12, 2025 |
| Times taken | 32 |
| Average score | 40.0% | Report this quiz | Report |
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1. y'=3x²-2x+1, y(0)=1
y=x³+x²+x+1
y=x³-x+1
y=x³-x²+x+1
y=x³-x²+1
2. y'=2e^x, y(1)=2e
2(e^2x)
2e(e^x)
2(e^x)
2(e^x)+2e
3. y'=y, y(0)=5
y=5
y=e^(5x)
y=5(e^x)
y=5x+5
4. y'=2y, y(0)=1
y=2(e^x)
y=e^(2x)
y=2(e^x)+1
y=(e^2x)+1
5. y'=y², y(0)=1
y=ln(x+1)
y=ln(x-1)
y=-1/(x+1)
y=1/(1-x)
6. y'=2xy, y(0)=2
y=e^(2x)
y=2(e^x²)
y=2(e^2x²)
y=2(e^x)
7. y'=x+y, y(0)=1
y=(e^x)-x
y=2(e^x)-1
y=(e^x)-x-1
y=2(e^x)-x-1
8. y'=-2y+(e^x)-1, y(0)=11/6
y=(1/3)(e^x)+(3/2)e^(-2x)
y=(11/6)(e^x)+2e^(-2x)
y=(1/3)(e^x)+2e^(-2x)-1/2
y=2e^(-2x)-1/6
9. y'=e^y, y(0)=1
y=1/(x-1)
y=-ln(-x+1)
y=1/(-x+1)
y=-ln(-x+(1/e))
10. y''-y=0, y(0)=2, y'(0)=4
y=3(e^x)-(e^-x)
y=3(e^ix)-(e^-ix)
y=4(e^ix)-2(e^-ix)
y=(e^x)+(e^-x)
11. y''-2y'+y=0, y(0)=4, y'(0)=11
y=4(e^2x)+3(e^-x)
y=3(e^x)+(e^-2x)
y=2(e^2x)+2x(e^2x)
y=4(e^x)+7x(e^2x)
12. y''+y=0, y(0)=3, y'(0)=2
y=3(e^2x)-2(e^-2x)
y=3cos(x)+2sin(x)
y=3cos(x)-2sin(x)
y=3(e^x)-2(e^-x)
13. y''-y=x, y(0)=7, y'(0)=2
y=5(e^x)+2(e^-x)-1
y=2(e^x)+5(e^-x)-xe^x
y=5(e^x)+2(e^-x)-x
y=2(e^x)+5(e^-x)-x²
14. y''-y=e^x, y(0)=3, y'(0)=1
y=3e^x+e^(-x)-x(e^x)
y=(13/5)e^x+(12/5)e^(-x)-2x(e^x)
y=(7/4)e^x+(5/4)e^(-x)+(x/2)(e^x)
y=2e^x+e^(-x)+x(e^x)
15. y''-2y'+y=e^x, y(0)=5, y'(0)=7
y=5(e^x)+7(e^-x)+e^(ix)
y=5(e^x)+2x(e^x)+7e^(-x²)
y=5(e^x)+2x(e^x)+(x²/2)e^x
y=5(e^x)+2(e^-x)+(x²/2)e^x
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