dy 2. dx = x³(y – x)² +, Y1 = x,x > 0 y У1 — х, х > 0 dy 3. + 2y + y² = 0,yı = -2 - dx

Q: Find the general solution for (y + 1) dx + (4x - y)dy = 0

A:

Q: y(x²-1)dx + (x³+8y-3x)dy =0  when x=0, y=1

A: Given: 3y2(x2-1)dx+(x3+8y-3x)dy=0initial condition is x=0,y=1

Q: Obtain the particular solution of the DE: 4(3x + y – 2) dx – (3x + y) dy = 0; when x = 1, y = 0…

A: Gg

Q: H2. 2dy dy dr2 d²y dy :1 at x = 0. dx – 52+2y= 2x², y=7 and - dx

A:

Q: Let y = 4x2 + 4x + 3. Find the differential dy when x = 1 and dx 0.4 %3D Find the differential dy…

A:

Q: Find the differential dy. y = 5x2 / x-9       dy =

A:

Q: 0.1 0.2 dz dy dx 3-3 X-る りー-oハ そ--0,2

A:

Q: 67. = 2x − 7, y(2) = 0 dy dx dy 68. = 10 - x, y(0) = -1 dx 1 69. dx + x, x > 0; y(2) = 1

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 1. (2xy² + ye*)dx + (2x²y + ke* – 1)dy = 0 2. (6xy³ + cos y) dx + (kx²y² – x sin y) dy = 0 %3D

A:

Q: Let y = 5x² + 5x + 3. Find the differential dy when x = 1 and dx = 0.1 %D %3D Find the differential…

A: Topic = Derivative

Q: Find the general solution for (3/y-6/x)dx - (3x/y^2 - 7/y)dy

A:

Q: integral of (y^2-14y+5) / y(y-1)(y-5) dy

A: ∫y2-14y+5yy-1y-5dySubstitute u = y-1=∫y2-14y+5yy-1y-5dyApply the Sum Rule:…

Q: I-x² f (x, y, 2) dz dy dx 1-x² Jo

A: we have to find the region of integration

Q: Let y = 3x² + 3x + 4. ind the differential dy when x = 4 and dx = 0.4 ind the differential dy when x…

A: Given query is to find differential at given point.

Q: dy 2. Given: x y = 2x-3y + 2 and- 3D3 %3D dt dx when x = 2 and y = 1 dt Find:

A: Consider the equation.

Q: QI Find for dx dt dy 4e - 5x'e dx dy 3re + 5x'e" dx O 2, dy - 2e + 4xe dx dy 2xe dx dy dy 5x'er dx…

A: We have to compute dydx, where y=∫x6x5et2dt. Comparing the given integral with the equation…

Q: 4 I. dx3, (d³y\ dy + 2- dx = sin x *+ O) + = In y. 3 II. dx dx dx d³y III. dx3 d²y , dy -2 + dx2 = x…

A: To identify which of the given differential equation is linear.

Q: 4) (x- y)dx+(3x+ y)dy =0, when x = 2, y = -1 5) (3x - 2 y²) y'= 2.xy, when x = 0, y =-1

A:

Q: 1. Separating the variables dy 1 x(y- 3) =D4y dx %3D

A: In the separation of variables method of solving the differential equation, the different variables…

Q: 2. ( 3 x - 3 y - 2) dx - (x - y + 1) dy = 0

A:

Q: dx -- 2 = 3y - 2 when x = 1, y = 1 dy

A: the given differential equation is: ydxdy-2=3y2-2 it is given that when x=1,y=1 we have to find…

Q: 2 Solue Bor メ= o-5 dx = y X (6) = 0 dt dy =_X yo) =I %3D

A: As per bartebly Guideline we can solve only one question.. Hope you understand

Q: x+y, 9- (e* + In y)dx + (- )dy = 0 y +(x* + y*)e°'dy = 0 10- x(1+e')dx

A:

Q: 4. (x +y- 4) dx - ( 3x-y-4) dy = o when x=4, y=!

A:

Q: Find the differential dy when x = 2 and dx = 0.1 Find the differential dy when x = 2 and dæ = 0.2

A: ddxtanx =sec2x ddxxn=nxn-1

Q: dy 21+ dr2 (vii) dy\2] & (dy\- da2 \dx². (viii) = 0. (ix) () z\ip, + 5y3 = x. dx.

A: (vii) The equation given is d2ydx2=21+dydx232. Squaring both sides. d2ydx22=41+dydx23 Order = 2…

Q: dy 2. if y = In(x² + 1) Then at x=1 %3D dx 2- 2 In 2 2- 1 1- 4- 1/2

A:

Q: dy 1- dx e-x-y-2 У (0)- -2 dy 2- dx ylny y(0)=e? 1+x2

A:

Q: (1 + Iny-) (;++i" y) dy = 0; 7. dx + y(2) = 1 Ans: In y+x+xIny-=0

A: The given differential equation is  1+lny-xy dx + xy+x22y2+3yln2y dy =0   ;  y(2) =1 Compare with…

Q: dy 1- dx e¯x-y-2 y(0)= -2 %3D dy 2- dx ylny %3D 1+x2 y(0)=e²

A: 1. ddxy=e-x-y-2,   y0=-2A first order separable ODE has the form of Ny·y'=MxRewrite, we get eyy'…

Q: d’y_2dy 3 y=2sin°(x) dx Determine the general solution of 2 dx

A: We have to determine the general solution of the differential equation…

Q: 5/xy dy -2, х, у» 0 dx y =

A: See the details solution in below

Q: 1 dy 2 - Y = 0 y =x*prove that - 2)- = 0 y dx

A: Given, y=xxTake log on both sides,lny=lnxxlny=xlnxDifferentiate on both…

Q: Using separation Variable. 1.) In x dx/dy = 2 / xy^3

A: Given differential equation lnxdxdy=2xy3

Q: 3. Obtain the Particular Solution when x = 4 and y = 1 (x+ y - 4)dx - (3x- y – 4)dy = 0 %3D

A:

Q: dy y-x General solution of = dx y+x

A: Solution:

Q: y=Ax+Dx^B is the particular solution of the first-order homogeneous DEQ: (x-y) = 5xy'. Determine…

A: Given differential equation, 5xdydx=x-y,  x=3,y=6 dydx=x-y5x put, y=vx dydx=v+xdvdx now put values…

Q: (2xy + x²)dy + (2xy + y²) dx = 0 A2 (3x² + 2xy) dx + (x²) dy = 0 *A3 (3x²y³ + 3 sin x + 4y) dx +…

A: Disclaimer: SInce you have asked to solve only question 3, this question has been solved only.…

Q: d²y dy + y dx 0, on 0 < x < 1 dx2 y(0) 0, y(1) 1,

A: Claim:- Solve the following boundary value problem for the function y=y(x,ɛ), where ɛ&gt;0, ε…

Q: d²y – 4y = 0 dy, - (at x = 0) = 4 dx а. dx? y(0) = 2; - d²y b. 5- dx2 sdy dy - (at x = 0) = 0 dx +…

A: To solve the given differential equations.

Q: y(x^2 + y^2)dx + x(3x^2 - 5y^2)dy =0 when x=1, y=1 homogenous eq

A:

Q: y² cos x - 3x3y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e x² - 1) dy = ((1 + x)2 -…

A:

Q: dy - 2-y ; y(0) =1 а. dx dy -1-y ; y(0) = 0 b. dx a = y sinx ; y(7)=3 dx с.

A: Answer

Q: 2. y' = y sec x ; 3. у(3x3 — х + у)dx + x?(1 — х?)dy %3D 0 4. у(2х — у + 1)dx + x(3x — 4у + 3)dy — 0…

A: 2) y'=y secx this can be written as dydx=y secx⇒dyy=secx dx integrate the function ∫dyy=∫secx dx…

Q: Find the differential dy. x + 2 y = 9x - 1 dy =

A: In this question we have to find we have differentiation of y.

Q: 2x - y + 5) dx - (2x + y) dy = 0 where x= 3, y=7

A: Let's find.

Q: +7 -3y = 20 sin (x), y(0) = - 1, y(0) = 2, dy.3y %3D Q5 5 dx dx

A:

Q: Obtain the particular solution when x = 1 and y = 1 y(x^3-y^-5)dx-x(x^3+y^5)dy=0

A: Here is the solution of the given differential equation.

Q: *= 1+?-,y = -x²,x > 0 2. = x³(y – x)² +2, y1 = x,x > o у 1. %D = x³ (y – x)2 + dx , Υ1 - x, x > 0 dy…

A:

Q: 3y(x2 - 1)dx+(x +8y–3x)dy= 0 when x= 0, y=1 |

A: Given: 3y(x2 −1)dx+(x3 +8y−3x)dy= 0 when x= 0, y=1