Problem

Write the following first-order differential equa…

00:54

Problem 213 Medium Difficulty

Write the following first-order differential equations in standard form.
$$
y^{\prime}=x^{3} y+\sin x
$$

Answer

$y^{\prime}-x^{3} y=\sin (x)$

Related Courses

Calculus 2 / BC

Calculus

Chapter 4

Introduction to Differential Equations

Section 5

First-order Linear Equations

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

Watch More Solved Questions in Chapter 4

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

Video Transcript

in our problem we meet must take the first order differential equation. Why prime equals execute y plus sign of axe and write it in standard form. The beginning part of this problem is to recall that center for minutes I've labeled it in green. On the right hand side, zoom us up. Here is white crime by itself, plus p of x times y on the left hand side equals Q Becks on the right hand side. So let us inspect how our equation matches or does not match this form. So beginning. Let us notice that we desire to have y primed by itself on the left hand side. And indeed, that's how did Piers now? So our goal will be to not manipulate this term. Next, we need to have all the terms and involved Why in a linear fashion on the left hand side, I say linear fashion just means why to the first power. So which terms over here involved wide in the first power? Well, this term right here involves wide of the first power in a sign of X dozen. So I want to get all the terms involving Why did the first power on that left hand side. So let me move it over minus X cubed. Why? Equal sign of acts and then next notice. I want y prime plus p of x y so I can rewrite this and a little bit of way that's more matching of standard form is I can write it like this. I just putting plus and then the negative just wipe aren't plus Snegur execute. Why? Equal sign of X And now here you can clearly see what p of X is p of X. Is this term right here? So we have got all over than your terms involving. Why in the left hand side and next. You know, um, of the terms not involving, why just acts on the right hand side. And indeed these the sign of excess only terms not involving why or why prime for that matter. And it's on the right hand side by itself. So this right here is our final answer. The box it and we are done

We have video lessons for 73.77% of the questions in this textbook