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For the following problems, find the general solu…

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Problem 208 Problem 209 Problem 210 Problem 211 Problem 212 Problem 213 Problem 214 Problem 215 Problem 216 Problem 217 Problem 218 Problem 219 Problem 220 Problem 221 Problem 222 Problem 223 Problem 224 Problem 225 Problem 226 Problem 227 Problem 228 Problem 229 Problem 230 Problem 231 Problem 232 Problem 233 Problem 234 Problem 235 Problem 236 Problem 237 Problem 238 Problem 239 Problem 240 Problem 241 Problem 242 Problem 243 Problem 244 Problem 245 Problem 246 Problem 247 Problem 248 Problem 249 Problem 250 Problem 251 Problem 252 Problem 253 Problem 254 Problem 255 Problem 256 Problem 257 Problem 258 Problem 259 Problem 260 Problem 261 Problem 262 Problem 263 Problem 264 Problem 265 Problem 266 Problem 267 Problem 268 Problem 269 Problem 270 Problem 271 Problem 272 Problem 273 Problem 274 Problem 275 Problem 276 Problem 277 Problem 278 Problem 279 Problem 280 Problem 281 Problem 282 Problem 283 Problem 284 Problem 285 Problem 286 Problem 287 Problem 288 Problem 289 Problem 290

Problem 267 Medium Difficulty

For the following problems, find the general solution to the differential equations.
$$
y^{\prime}=2^{x}+\cos ^{-1} x
$$

Answer

$y=\frac{2^{x}}{\ln (2)}+x \cos ^{-1}(x)-\sqrt{1-x^{2}}+C$

Related Courses

Calculus 2 / BC

Calculus

Chapter 4

Introduction to Differential Equations

Section 5

First-order Linear Equations

Related Topics

Differential Equations

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Watch More Solved Questions in Chapter 4

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Video Transcript

for about five. Number 2 67 Whereas to solve this different equation, this is a separable differential equation. So if I look at it, D y dx is equal to two to the X plus the art co sign of X. So I could write this as D Y is equal to two to the axe does the inverse coastline of X dx. Then I can integrate both sides of that equation and that will give me why is equal to. And so this is to to the X over the natural log of to and then to integrate the inverse co sign. This is going to be plus X in verse co sign of X minus the square root of one minus X squared, plus a constant of integration. So that is the solution toothy different your question.

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Gilbert Strang,

Calculus

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