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Recent questions in Second order linear equations

Javion Kerr 2022-03-22

Find the general solution y(x) of the following second order linear ODEs:
$y^{″} - 4 y^{'} + 5 y = 0$

London Douglas 2022-03-22

Find the general solution y(x) of the following second order linear ODEs:
$y^{″} - 4 y^{'} + 4 y = 0$

Anahi Solomon 2022-03-22

Which of the following is not a solution of $y^{″} + 4 y = 0$
(A) $4 \cos (2 x)$
(B) $5 \sin (2 x)$
(C) $\sin (2 x) \cos (2 x)$
(D) $4 \cos (2 x) + 5 \sin (2 x)$

Beryneingmk39 2022-03-22

Detemine whether the equation given is a solution to the corresponding differential equation.
$y = C_{1} e^{- 1.25 t} + c_{2} e^{- 5.5 t} - 16;$
$y^{″} + \frac{27}{4 y^{'}} + \frac{55}{8 y} = - 110$

afasiask7xg 2022-03-22

Find the particular solution to the initial value problem
$y^{″} - 2 y^{'} + y = 0, y (0) = 1, y^{'} (0) = - 1$

zatajuxoqj 2022-03-22

Find the general solution of the following differential equation (where primes denote derivatives with respect to x):
$y^{″} + 8 y^{'} + 16 = 0$

Ashleigh Shaffer 2022-03-22

Solve the given differential equation by undetermined coefficients.
$y^{″} + 4 y = 4 \sin (2 x)$

Caerswso1pc 2022-03-22

Solve the equation:
$y^{″} + 2 y^{'} + 2 y = 0, y (\frac{π}{4}) = 2, y^{'} (\frac{π}{4}) = - 2$

Harley Ayers 2022-03-22

Find the solution of the following initial value problem:
$x^{″} (t) - 7 x^{'} (t) + 10 x (t) = 0, x (0) = 2, x^{'} (0) = 3$

Zack Mora 2022-03-22

Identify the auxiliary equation of the following differential equation along with its roots and the two fundamental solutions.
$y^{″} + 6 y^{'} + 8 y = 0$

anadyrskia0g5 2022-03-22

Solve the equation
$y^{″} - 4 y = 2 + 3 x - x^{2}$

Caerswso1pc 2022-03-22

Find the particular solution of the following linear second-order inhomogeneous differential equation
$\frac{d^{2} y (t)}{{d t}^{2}} - 2 \frac{d y (t)}{d t} + 4 y (t) = 3 t - 4$

aidinacol7 2022-03-22

Solve the following differential equation
$y^{″} + 4 y = \cos x \sin x$

y^ prime prime -3y^ prime +2y=10 sin x+2 cos 2x . Find a general solution of the following

Let λ ∈ R be a parameter. We consider the ODE with conditions to the limits. y + λy = 0, y(0)= 0, y(1)=0 Explain why the existence and uniqueness theorem does not apply.

fumefluosault7pa 2022-02-14

Find the complete solution of y" - 2y' + 2y = sin2x + e* cos x .

Oberlaudacu 2021-12-20

If we consider the equation
$(1 - x^{2}) \frac{d^{2} y}{{d x}^{2}} - 2 x \frac{d y}{d x} + 2 y = 0, - 1 < x < 1$
how can we find the explicit solution, what should be the method for solution?

hvacwk 2021-12-19

Find equations of the tangent line and normal line to the given curve at the specified point. $y = 2 x e^{x}, (0, 0)$

Painevg 2021-12-18

Let $y (t)$ be a nontrivial solution for the second order differential equation
$\ddot{x} + a (t) \dot{x} + b (t) x = 0$
to determine a solution that is linearly independent from y we set $z (t) = y (t) v (t)$
Show that this leads to a first order differential equation for $\dot{v} = w$

veksetz 2021-12-17

I need to solve the following differential equation
$x^{2} y^{″} + (a x - b) y^{'} - a y = 0$
with $a, b > 0, x \geq 0$ and $y (0) = 0$ . The power series method will fail since there is a singularity at x=0, while the form of the equation does not conform with the Frobenius method.

Dealing with second-order linear equations is quite complex for post-secondary algebra students who have to provide such equations for statistical analysis where calculus is involved. It’s a reason why linear equation examples help with the system of linear equations, especially when it has to be implemented in Sociology, Engineering, or even Business Management. It is a reason why linear equations word problems have also been offered below as students cannot approach them without some linear equations solver that would contain an explanation with details. You can see answers to questions and learn how linear equations and inequalities can be solved.

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