Concept explainers
Implicit solutions for separable equations For the following separable equations, carry out the indicated analysis.
- a. Find the general solution of the equation.
- b. Find the value of the arbitrary constant associated with each initial condition. (Each initial condition requires a different constant.)
- c. Use the graph of the general solution that is provided to sketch the solution curve for each initial condition.
41.
Want to see the full answer?
Check out a sample textbook solutionChapter 9 Solutions
Calculus: Early Transcendentals, Books A La Carte Edition (3rd Edition)
Additional Math Textbook Solutions
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Precalculus Enhanced with Graphing Utilities (7th Edition)
- Find the unknown value. 27. y varies jointly with x and the cube root of 2. If when x=2 and z=27,y=12, find y if x=5 and z=8.arrow_forwardSolve for Z. X= (Y-Z) 3arrow_forwardConsider the following. x² + y2 : = 16 (a) Find two explicit functions by solving the equation for y in terms of x. Y = (positive function) Y2 = (negative function) (b) Sketch the graph of the equation and label the parts given by the corresponding explicit functions. y y 5 X -5 -5 y y 5 5 -5 -5 (c) Differentiate the explicit functions. dy/dx = + (d) Find dy/dx through implicit differentiation. dy/dx = y Is the result equivalent to that of part (c)? Yes No O Oarrow_forward
- B. Determine the solution set of the following equations using exact equations. 1. 3x (xy - 2)dx + (x + 2y)dy = 0arrow_forwardQ1: Find the general solution of the following equation. ỹ+ 2y + y = cos² xarrow_forwardB) Find the approximate roots of the following equation: f (x) = x3 – 8 = 0, on the closed interval [0,3]. %3D %3Darrow_forward
- 5. Exact Equations: Solve the equation 3x (xy – 2) dx + (x³ + 2y) dy = 0arrow_forwardFind two explicit functions by solving the equation for y in terms of x, (b) sketch the graph of the equation and label the parts given by the corresponding explicit functions, (c) differentiate the explicit functions, and (d) find dydx implicitly and show that the result is equivalent to that of part (b). x2 + y2 − 4x + 6y + 9 = 0arrow_forwardClassify the equations below as separable, linear, exact, or none of these. Notice that some of the equations may have more than one classification. (x²y + x² cos(x)) dx = x³dy = 0 (yety + 2x) dx + (xey - 2y)dy = 0 y²dx + (2xy + cos(y))dy = 0 Odr+ (3r-0-1)d0 = 0arrow_forward
- Solve the Equaiton for y. 10/4y + 8/2 = 2y - 2arrow_forwardSolve for y in terms of x (isolate y on one side of the equation and put all the other variables and constants on the other side). Show your step-by-step solution. 4. 2x3 + 3xy? +y = y² – 1 5. e?y =sin sin (x + y)arrow_forwardDetermine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y(4) + 2y" + 2y" = 2e" +5te 4t +et sin t NOTE: Use J, K, L, M, and Q as coefficients. Do not evaluate the constants. Y(t) =arrow_forward