Integrate using the method of trigonometric substitution. Express your final answer in terms of the variable x. (Use C for the constant of integration.)       dx (x2 − 36)3/2

Q: Determine whether the equation is exact. If it is exact, find the solution.…

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Q: Solve this differenttial equation.   By help of integrating factor. (3xy+6y^2).dx+(2x^2+9xy).dy=0

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Q: Which constant c would best be described as a constant of integration? c +1 Secx=a

A: The indefinite integral always results a constant of integration.

Q: Integrate the following expression, and solve for the constant of integration using the fact that y…

A: To solve for the constant

Q: 6. (2x + 3y)dx + -x)dy 0 %3D

A: Consider the given equation as 2x+3ydx+y-xdy=0

Q: x? -dx ² 2 Integrate by trigonometric substitution: V7 -x

A: We have to find the integral

Q: d) fe'cos( 41)

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Q: (D3 + D - 10) y = 29e4x

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Q: Solve the ODE by finding an integrating factor for exact equations. (2xy2+3x)dx - 2xydy=0

A: Recall: If the equation M(x,y)dx +N(x,y)dy=0 is not exact and ∂M∂y-∂N∂xN is a function of x only…

Q: fo 5x cos(a2) dx (x²) dx

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Q: COs 2.r dx x² + 2x + 2

A: In this question, we find the principal value of the integral by using residue theorem

Q: /x[cosh?( 2x²) – sinh²(2x²) ]dx is equal to (A) x?dx B) None © Sar dx (D 4 xdx E xdx

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Q: Find an integrating factor and solve the given equation. (15x + ²) + (5²+ 15y dy X dx

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Q: Q6// find the general solution (sin-ix+- 1 dx + sin-1xdy 0

A: Note the following result of integration. We will use it in the solution :

Q: Evaluate the integral (Trigonometric Substitution) x*dx (x² + 1)²

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Q: Find an integrating factor and solve the given equation. (12x + 3) + (4²+¹2) = 0 12y dy dx

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Q: Using undeterminate coefficien ts, Solve : d'y _q dy =9 e + 82* dx 3 3X 3 dx

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Q: Evaluate. (Use C for the constant of integration.) x2 dx (1 – 25x²)3/2

A: Given,          ∫x21-25x232dx

Q: (1+ y²)dx + (x²y + y)dy = 0

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Q: Find an integrating factor and solve the equation (sin x+ e° ) dx + cos xcdy =0.

A: According to question sinx+eydx+cosxdy=0

Q: cos a eT dx ¤ dx Csc x

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Q: CSc x e dx Cos x

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Q: c). Using an integrating factor solve the equation dy , 4. +y= 3x dx

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Q: dx Q3: A) Find the integration: : XV4 X2–1

A: given∫1x4x2-1dx substitute u=4x2-1 dudx=4x4x2-1 dx=4x2-14xdu

Q: Q/ Solve the differential equetion (x²4)dy=zxy dx

A: As per our guidelines we need to solve only one question. Please repost the remaining questions as…

Q: B: Solve the following integrations: a- fx³e-2x dx b-fdx +10 c-f 3sec³x. tanx dx

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Q: d³y d?y dy dx3 dx3 - y = 4 sin x dx

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Q: Using integrating factor, solve  dy/dx - 3y = 6

A: To find the solution of the differential equation.

Q: / [cosh²(2x²) – sinh?( 21²) ]dx is equal to A B dx c) None D x²dx E xdx

A: Let's find.

Q: Using the method of changing independent variable, solve (1+ x)²y" + (1 + x)y' + y = 4 cos(ln(x +…

A: Solve the differential equation            (1+x)2y''+(1+x)y'+y = 4 cos(ln(x+1))

Q: 50. g(x) 52. f(x) = xe* 54. y = sin²(e³x+!) %3D

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Q: solve d 3 d'y = sin2x dx dx

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Q: By using appropiate substitution, solve dy hpT i. x2 dx 1 = xy – y² ii. – 2. (2х + у)е2»+у | dx

A: Consider the provided question, (b) (i)

Q: -4 dx 7). Si: xVx-1 I-x^x

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Q: Find a value for the constant A so that: 4(3x + 5)' dx : (3х + 5)" + C A

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Q: y (2xy + y²) dx + x (y² − x) dy = 0

A: According to question given:y(2xy+y2)dx+xy2-xdy=0y(2xy+y2)dx=-xy2-xdydydx=-y(2xy+y2)xy2-x

Q: Using Integrating Factor by Inspection, solve: (y − xy²) dx + (x + x²y²) dy = 0

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Q: Solve the equation (1 + x cosy) dx - x²siny dy = 0 using substitution.

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Q: Solve by finding an I.F 1. xdy- ydx= (x* + y° \dx

A: given equation is                                xdy-ydx=(x2+y2)dx let…

Q: iven the ODE, solve: x(x + 4)*dy + [y(x+ 4)* – 3x*y³]dx = 0

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Q: QI: Solve the following DE: e*dx-ydy 0y(0) = 1

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Q: B: Solve the following integrations: a- fx³e-2x¹ dx b-fdx c-f 3sec³ x. tanx dx marks

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Q: (2x2 + 3у? — 2)dx — 2хy dy %3D 0

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Q: Test for exactness and find the general solution. (2xy – sin x) dx + x²dy = 0

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Q: Solve using method of undetermined coefficients d?x d3x + 6 dt3 dt2 d?x + 12 dx dx + 8x = 0 when t =…

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Q: X CSC -y|dx + xdy=0. Obtain the general solution of

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Q: (2xy - x + 2y - 1) dx + (8x² y² -2x + 4xy2 - x) dy = 0

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Q: To integrate x3x² 842 242 Ox we apply integration by parts and in the form u dv, dv is set as: dx'

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Q: (2xy - x + 2y - 1) dx + (4x²y² - x² + 4xy² - x) dy = 0

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Q: Solve for the differential

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