The Bernoulli's equation +y tanx = ysecx can be made linear upon multiplication by. and substitution of (A) -y-2 and z=y-1 B -2y-3 and z=tanx -y-2 and z=tanx -2y-3 and z=y=2

Q: The point on the curve y = 2-x nearest to (3,2) is (1,1) (0,2)

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Q: Give the general solution to the equation x' Ax where A = %3D

A: To find the general solution of the given system, first we find the eigenvalues and corresponding…

Q: from y = ae + be %3D 2.

A: y=ae4x+be-4x ....(1) Differentiate both side w.r.t x dydx=4ae4x-be-4x        ....(2) From (1) and…

Q: Find the general solution of y' = y secx

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Q: If -y = xy - 3x then find d at the point (-2,6) in simplest form. 1

A: As we know that the differentiation of:- dxndx=nxn-1 (fg)'=f'g+fg' fg'=gf'-fg'g2

Q: Find two linearly independent solutions to x2y′′+x(3−2x)y′+(1−2x)y =0 on (0,∞).

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Q: Use chain Rule to find for 2. y = . +x²+x+1 I.W | 3. y = estn 3x Н.W

A: We have to find dydx using chain rule for the given function: 2.  y=1x3+x2+x+13.  y=esin 3x We know…

Q: aber of linearly 1 is

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Q: Find the equation of the line normal to x3y-2xy2= - 4 at the point (-2,1)

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Q: Find an equation of the secant line containing (1, f(1)) and (2, f(2)). f(x) = x² - 2x

A: Rule:-equation of line passing thraught (x1,y1) and (x2,y2) is y-y1=y2-y1x2-x1(x-x1)

Q: If y2 is positive, then y1 + y2 will lie _______ y1 by a distance equal to ____.

A: Consider a function y=sinx+1. Here y1=sinx and y2=1>0positive.

Q: Čonvert the following equation into standard form. 7x y = - - 3 %3D 2 [?]x+ [ ]y = [ ]

A: The given equation is y=-7x2-3

Q: Find the local extreme values of ƒ(x, y) = x2y on the line x + y = 3.

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Q: Obtain two linearly independent solutions valid near x = 0 x2y" + x(x-1)y' + (1-x)y = 0

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Q: Obtain two linearly independent solutions valid near x = 0  xy" + x(x - 1)y' + (1 - x)y = 0

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Q: The equation of the line tangent to the curve y=3x+4/4x-3 at the point (1,7) is  a) y - 25x=-18 b) y…

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Q: Parallel to x + 2y = 0; (1, 2) on line

A: To find the equation of line paralley to x+2y=0 and (1,2) is on the required line.

Q: Find an equation of the curve that passes through the point (0, -7) and whose slope at the point 2x…

A: we have to find the equation of the curve

Q: Find the point on the line y = 3x + 4 that is closest to the origin. (x, y) = |

A: To find - Point on the given line closest to the origin.

Q: Find ƒyxyz if ƒ(x, y, z) = 1 - 2xy2z + x2y.

A: Given that, fx, y, z=1-2xy2z+x2y           ...(1)

Q: For which values of the constant c is a linear -日 combination of a and where a and b are 62…

A: We have to find values of c

Q: Find y" * y" at (1,1) of x'y =1

A: We have to find derivative

Q: 3. Which equation passes through the point (1, -2) and is perpendicular to y = x O y = 3x - 1 O y =…

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Q: Find the point on the line y = 2x + 3 that is closest to the origin. (x, y) =

A: The perpendicular drawn from the origin to the line represents the shortest distance.

Q: (i) Find the covariance of Y1 and Y2, Cy, Y,

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Q: х2у" + x(x-1)у' + (1-x)у %3D 0

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Q: Find the equation of th line perpendicular to the line 3y=2-4x and passing through the point (4,7)

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Q: Solve by Chain Rule 8 poir f(y) = /2y + (3y+ 4y²)³ %3D

A: Here clearly not mentioned, what to do with this question, but as we know chain rule is applied to…

Q: The point (0, 1) has the distance from the line defined by y = -2x – 1

A: Solve for distance

Q: у" — у' — х %3D 0

A: We are given: y'''-y'-x=0⇒y'''-y'=x Auxiliary equation is : m3-m=0⇒m(m2-1)=0⇒m=0, 1, -1 Hence,  CF=…

Q: Find an equation of the curve that passes through the point (1, 1), and has the given slope y′ = −…

A: y'=-9x16yPasses through (1,1)Formula∫xndx=xn+1n+1+C

Q: Find the homogenous linear equation with real, constant coefficients that is satisfied by:…

A: Given that  Required differential equation is satisfied by   y= 6 + 3xe^x - cos x

Q: Find the point on the line y = 4x + 3 that is closest to the origin. (x, y) =

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Q: 2: Show that the line equation passing through two distinct points (a1, b1) and (a2, b2) can be…

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Q: Find the point on the line y = 3x + 4 that is closest to the origin. (x,y)=

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Q: Find an equation of the curve that passes through the point (0,1) and whose slope at (x, y) is 11xy

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Q: S sec 2ydy

A: Topic:- integration

Q: Find two linearly independent solutions of the equation (x-1)y"+y=O for |x|<1

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Q: utilize the characteristic equations method to solve the equation y''-5y'+3y=0 y(0)=3, y'(0)=-1

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Q: A particle moves on a vertical line so that its coordinate at time t is y=t3 - 12t + 3 , t>0. When…

A: (b)        y = t3 -12t+3    y1 =3t2 - 12 = v(t) when particle moving up means v(t)&gt;0    3t2…

Q: The line whose slope is 3 is tangent to the curve y=x² + 3x + 2 at the point, O (3,-2) O (-3,2) O…

A: The line whose slope is -3 is tangent to the curve y=x2 +3x+2 at the point. Here slope and line…

Q: Find the equation of a line parallel to x = -8+ 2y that passes through the point (8, –2). Oy = -x –…

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Q: slope of the tangent to the curve y2x+ y2x2 =6at (2,1) is

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Q: - 6х + 2у, dt dy -3х + 1у dt

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Q: Find the equation of the family of curves whose slope at any point (x,y) is given and which passes…

A: To find the equation of family of curves whose slope is given .

Q: Solve for y in terms of x and z. z = xy

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

Q: Find the general solution of the lines 3y (즉 + 2-2)dx + (2x- 3 +1 )dy = 0 - 2 )dx + ( 2x - +1 )dy =…

A: x2+3y4-2dx+2x-y2+1dy=0To Find: The general solution of the lines.

Q: Find the slope of the curve x3y3 + y2 = x + y at the points (1, 1) and (1, -1).

A: Given,

Q: Explain why an equation Ax = b has a solution if and only if b is orthogonal to all solutions of the…

A: