7. Use the convolution integral (see Example 2 in Boas' Sec. 8.10) to solve the following differential equation y" + 5y +6y=e=² with initial conditions yo yo = 0. = -2t (1)

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Q: 4. What is the differential equation of the given functions? • y = Ce-* + Cze-2x + x y = Ce2* +…

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Q: 2 4 Solve the differential equation y dx - 2(y - x) dy = 0. If y = 1 when x = 3, determine x when y…

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Q: An L-R-C circuit has the following differential equation: (q = charge on capacitor) with q (0) = 1…

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Q: –3x Show that the function y= e²* + e* satisfy the differential equation y"+y'-6y=0

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Q: {x ER: 2x + 31+x=0} = {-6, -2}

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Q: Example: Consider the differential equation 3t²y" + 11ty' – 3y = 0. | Is y(t) = a solution?

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Q: y" – 3y' - 4y = 3ez* у" - Зу'- 4у 2 sin x

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Q: Q2) Use Separation of Variables for solving the following parnial differential equation u(x,0)- (x)…

A: given ∂u∂t=k∂2u∂x2-u ux,0=fx  , u0,t=0  ,  -∂u∂xL,t=uL,t claim- to solve the differential equation…

Q: 2. Solve the following 4th order linear differential equations using undetermined coefficients: y…

A: We need to solve D.E.

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Q: 2yy"=1+y'².

A: We have given differential equation ,  2yy'' = 1 + y'2 Here , substitute y' = u ⇒ y'' = u u'  Thus…

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Q: Show that if the roots of the auxiliary equation of a differential equation are r = p± qi, then the…

A: The given roots are r=p±qi. Show that the differential equation itself is y''-2py'+p2+q2y=0. Here we…

Q: Solve the given differential equation by using an appropriate substitution. x - (1+ x) y = xy² dx

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Q: (D – 3D + 2) y = (1+ e-")?

A: I am attaching image so that you understand each and every step.

Q: Consider the differential equation: 17y' one of the following is the value of X ? 17 17 -17 0-1 17 =…

A: Given that   is the general solution of the differential equation   ---------(1)…

Q: xy! √√x²+ x² + y² +4

A: Here we have to use substitution to find the solution of given differential equation.

Q: Q2) Solve the following differential equation a²y 2 - 64 y = -105 with the conditions y(0) = y(1)…

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Q: 9. Find the general solution of the differential equation y" - 2y' = sin 4x.

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Q: 1. Solve the differential equation (2xy² - x³)dy + (y³ − 2 yx²) dx = 0.

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Q: 4. Solve the differential equation by separable variable method, (ex + e-*): dx e-*) = y?.

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Q: 11. Consider the differential equation - 7y = 0 the roots are equal to: %3D

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Q: 8. Solve the differential y" + 6y +9y equation by variation of parameters. for a > 0.

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