1) Find ôz|ôu and ôz/ôv for z= 4e* In(y), x=ln(ucos(v)), y=usin(v) at the point (u, v) = (2, 7 | 4). %3D Ans. Z, = v2(1n2+2), z, = -2/2(In2– 2)

Q: How do I get 2y*dx/dt + (-4xy + y' * x^2) = 0 and y' = (1/ x^2)(2xy + y - 1)?

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Q: How many real valued solutions over (-1,1) to the following ODE?

A: given odinary differential equation  y'=x1-y'+ylnlny'+eπxy claim-  to check how many solution does…

Q: * Find dy/dx for the function y=2 sin(3x) cos2x 4 sin (3x) sin (2x) - 3 cos (2x) sin (2x) O 6 cos…

A: We know that derivatives  general power rule is - d(xn)/dx = nxn-1. And d(sinx)/dx = cosx ;…

Q: 12. integrate (10x+6x +2x-6)dx

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Q: 8. Integrate S –x³Vx² + 2 dx

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Q: 13. y = A²x' - 3Bx %3D (x) ans : y' = 34A²X² - 3B %3D (x)

A: Given: Y(x)= A2x3-3Bx Differentiate y(x) with respect to x

Q: 2 13 y+y+y%3Dx"+4X+12%

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Q: 4) (e* + y)dx+ (2y + x)dy = 0 %3D

A: Hence, the general solution is                                            y=-x±x2-4(ex-C)2 Where C…

Q: What is an integrating factor of the nonexact DE dy/dx = 1/(2xy) -2y 2y e^(y^2) e^(-y^2) O NA

A: We have to find

Q: 3 L²T³ « 1 (12x3 - 27x²y²) dy dx

A: Given integration is ∫01∫13(12x3-27x2y2)dydx

Q: If x + y 1 Find dx O a. -1( y^2) where y^2 means y squared represents exponentiation Ob. 1/ (y^4)…

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Q: If y (x) = Ae^ikx for -L/2<xsL/2 normalize it, then A= 1. VI 10 2L .II O 1 L II O

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Q: ind the general solution for  Z_yy +Z=e^(x+y)

A: zyy+z=ex+y

Q: Calcule aw/ as si w= e*3y+z², x= 3s- sen(t?), y= cos(5s) – 4t; z= In(s² + tª). exzy+z² (6xy+…

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Q: 1. ò -2 dx 2. Ò x“ dx 3. Ò 5Vx dx 4. Ò 3/F° dx 5. Ò (3x* +5x³)dx

A: Here we use integration in the following: 1) ∫-2 dx2)∫x14 dx3)∫5xdx4)∫3x43dx5)∫(3x4+5x3) dx

Q: d(d Which of the following is the same as -台) dx dx dx None d'y (dy d'x dx C ddy D dx4

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Q: メ y= Ce + C,e , (-0∞, 0); g- y = 0, Y(0) = 0, y'o) = 1 %3D %3D %3D f=メ, f,0 =メ)f 11 2. A 4x-3x %3D…

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Q: This is a linear DE. If arranged to its form, what is the integrating factor? * (X^ 12y) ch -xdy = 0…

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Q: (? + 5 )2y = 3r(y² + 1)- -(a+ + 8x² + 9)y, y(1) = 0 4+8 (,? + 5),'

A: solve the given equation by separable method:

Q: integration Solve the following problems suox'+300)-dx on

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Q: Find dz/dx for the equitation xe^z +ze^y= x+y

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Q: Solve the equation y' = x^3 + y^3 / xy^2 fraction homogeneous first order ODE set v= y/x

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Q: Now, from 2 q (x, y) = -tan (²77) + g (4) partially diff⋅ w.s. to 'y' S (x, y) = Now, 28 (8,9) - 1+…

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Q: 6) а. Find dx if y%3 (n(x + Aj) - А2 х) (/5 В, - 7х) А131 A2=5 В1-4 B2=6 В3-2 DA-1

A: The given function is y = [ln (x + A1) – A2 x] (√5B1 – 7x). The given values are A1 = 1, A2 = 5 and…

Q: (iї) Зx' — 6х %3Dsin2t x(0) = 1 (iv) у" + 6у' + 13у %3D 0 У (0) %3 3, у'(0) 3 7

A: We have to find first complementary function and   particular integral and then add them, that will…

Q: y' + 4y = e^(4t) %3D

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Q: f'(x) = 3Xt7 21x 2X and FC) =G %3D Find FCx).

A: Integration formulae: ∫xndx=xn+1n+1+C∫12xdx=x+C∫enxdx=enxn+C

Q: O -(-1)'I and let Let In tan (a) for n = 0,1, 2 Int2 1) Show that In + Io+ (-1) for na an- An-1 %3D…

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Q: | Example 8.11. Evaluate the integral the error with the exact value. dx using Simpson's 1/3rd rule.…

A: Please find step by step solution below

Q: 00 2. It is well known that /e-* dx = VT . Use this fact to prove that / V- In xdx 2 -00

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Q: The integrating factor of the given DE are already given below. What is the value of “n” ?…

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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.