What is the solution to the initial value problem y" – 2y' + 10y = 0, y(0) = 3, y'(0) = 0 ? A) y = e3* (cos 3x + sin 3x) B) y = e* (3cos 3x – sin 3x) C) y = e2* (2cos 6x + sin 6x) D) y = e*(-cos 3x +3sin 3x) E) y = e3* (2cos x – sin x)

Q: Ou :? u =x +y +:, x=e" cos 21, y =e"21, : =e" = e" (cos 21-sin 4t +&t +8) +2e Ob. e (cos 21 - 2 sin…

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Q: Show that an implicit solution of 2x sin²(y) dx - (x² + 18) cos(y) dy = 0 is given by In(x² + 18) +…

A: Given that  Equation : 2x sin2(y)dx - (x2+18) cos(y) dy = 0 and Implicit solution : ln(x2+18)…

Q: Let f(x) = 8 cos x + 5 tan æ f'(x) =-8 sin(z) + cos(z)2 r(#) = 37 Find the exact trig values for…

A: Since, we have been given that f(x)=8 cos (x)+5 tan (x)Also, we have f'(x)=-8 sin (x)+5cos (x)2Our…

Q: (10) y = एस COS (5x) ) y' = ?

A: By applying the product rule for the differentiation.

Q: If the solution of y'' -4y' + 8y = 0  is in the form of y(x) = (e^(ax)) *(c1*cos(bx) + c2*sin(bx))

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Q: Find y'' if y=-6 cos x. OA. y' = 6 sin x OB. y' = 6 cos x OC. y'= -6 cos x OD. y'= -6 sin x

A: The function is given byTo determine: The expression of the second derivative of the function.Formul…

Q: 6. y cos5 (sin(2x)), y'=?

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Q: Solve 2(cos2x)y' + ysin(2x) = 4cos4x 0 =< x < pi/2

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Q: In implicit differentation problems it seems we treat x and y differently. For example, when we…

A: Recall: Chain Rule of differentiation :    If F(x)=f(g(x)) then ,   F'(x) = df(g(x))dx =…

Q: Select the general solution to the equation. y" + 16y = 0 %3D Oy= C1 cos(-4x) + c2 sin(-4x) Oy= cie…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.