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Practice: Linear DE

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Wize University Linear Algebra Textbook > Differential Equations

Basics of Differential Equations

6 Activities

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Q:\bf{Q:} Solve x2  ⁣dy  ⁣dx+3xy=1x^2 \dfrac{\de{y}}{\de{x}} + 3xy = 1
More Basics of Differential Equations Questions:
Find a solution to the differential equation
dydt=3y\frac{dy}{dt}=3y
where y(0)=6y(0) = 6 .
Solve the differential equation
dydx+(tan⁡ x)y =sin⁡x \frac{dy}{dx}+\left(\tan\ x\right)y\ =\sin x\
subject to y(2π)=π3.y\left(2\pi\right)=\frac{\pi}{3}.
Differential Equations
The functions y=x2+cx2y=x^2+\frac{c}{x^2}, are all solutions of equation: xy′+2y=4x2, x>0.xy'+2y=4x^2,\ x>0.
Find the constant cc which produces a solution which also satisfies the initial condition y(6)=5.y\left(6\right)=5.
Differential Equations
Find an equation of the curve that satisfies dydx=80yx15\frac{dy}{dx}=80yx^{15}and whose y-intercept is 66.
Differential Equations
Let y′=7xy'=7x. Find all values of rr such that y=rx2y=rx^2 satisfies the differential equation.
List all the values separated by a comma.
Differential Equations
Solve the differential equationdydx=4yx\frac{dy}{dx}=\frac{4y}{x},x>0.x>0.