dy + p(x) y = q(x) y" . If we substitution y = u' Given any Bernoulli DE the Bernoulli DE becomes a %3D dx Linear DE in x Homogeneous DE O. None of These Separable DE in x and y Linear DE in y

Q: + ( Xyz

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Q: To convert the nonlinear DE xy²y' = y³ – x³ to become a linear DE we use the substitution y= u"…

A: Given the nonlinear DE  xy2y' = y3-x3

Q: If sin (x – y) = x³ then dy 1s dx а) dx dy _ ycos(x – y) – 3x² хcos(х — у) dy_ cos(x – y) – 3x? b)…

A: Solution is given by using sum and difference identities of trigonometry as follows :

Q: If f(z, v) – 4z°y+ 8zy, then the total differential of f at z-1 and y - 1is: O df - 17 dz + 22 dy O…

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Q: If u(x, y) = e-2* sin(2y) and f(x) = u(x, y) + iv(x, y) is analytic, then v(x, y) = %3D %3D

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Q: Y. (y² cos x - y) dx + (x + y²) dy = 0

A: As per the company rule, we are supposed to solve one problem from a set of multiple problems.…

Q: 2. Find if y=x² + 3x-7 and x=2t+1. d²y dt2 3. Find dx and d²y dx2 if x = t - and y= 1+t 1² 1+t

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Q: Given f(x, y) = 4x²y then the total differential df %3D O 4xy dx + 4x² dy O 8xy dx + 4x² dy None of…

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Q: |Show that the substitution v = In y transforms the differ- ential equation dy/dx + P(x)y = Q(x)(y…

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Q: 1.1: If y2 = x² + 2xy, then dy y+x dx a) y-x b) 2x + 2y x+1 c) y d) - x corre None of the above ||

A: Given y2=x2+2xy

Q: X. 2. dx + cos y ) dy = 0 y A. xy - ysiny + cosy = C B. xy – ysiny - cosy = C C. xy + ysiny + cosy =…

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Q: Let z = e* + In( y), x = sin (uv), y° = cos (uv). 2 Determine at u = 1, v= 3

A: Topic- partial derivatives

Q: dy Given y = u? - 1 and x = u2 + 1, find dx

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Q: 2) Let 1 = f* cos y3 dydx. By reversing the order of integration of I, we get a. 1 = ²₂x cos y³ dx…

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Q: -2x + 3x -x) dr- (sin y + y e (y e + +3y e) dy 0. x(0) 1 D 2r-- O 2y - y+ xr e O x+ 2x-y e-3y e+3e–…

A: The given differential equation is,(y2e-2x+3x2-x)dx-(siny+ye-2x+3yey)dy=0, x(0)=1

Q: Write the linear DE of order one x²dy + (2xy-x+1) dx=0 in standard form A B D dy dx dy dx 1 2 +y(-)…

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Q: u-3 15) If y= u+4 and u = 2/x+ 2, find when x = 7 dx %3D

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Q: 10. f (x, y) = 1 sec(xy) in(rv)

A: Solution:-

Q: 1. dy dx \y+1 x2+1/ 2. " S"(sinx + cos2y) dx dy 3. S V(2x + y)" dx dy 1 3

A: Since you have asked multiple question, we will solve the first question for you.  If you want any…

Q: a When reduced to a linear DE of order one in z, the Bernoulli's equation dx becomes dz A + z( − 1)…

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Q: Which of the following DEs are first order linear DEs?

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Q: A) If w = 2 y et* – In z where x = In(t² + 1), | dw y = tan-1 3t and z= e3t. Find by Chain Rule dt

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Q: Let w = (sin(x) +7cos(y)) dy ^ dz + (z³ – y cos(x)) dz A dæ + 14xyz d A dy. Find dw. dw = dx A dy A…

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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.