ID

problem

ODE

18453

2

$x^2{y}^{\prime \prime }-\frac{x^2{y^{\prime }}^2}{2y}+4x{y}^{\prime }+4y=0$

18454

3

$y^{\prime }+cy=a$

18455

4

$y^{\prime \prime }+\frac{y^{\prime }}{x}+k^{2}y=0$

18456

5

$\sin \left(x\right)y^{\prime \prime }+y^{\prime }\cos \left(x\right)+ny\sin \left(x\right)=0$

18457

6

$y^{\prime }=\frac{\sqrt{1-y^2}\arcsin \left(y\right)}{x}$

18458

16 (a)

$v^{\prime \prime }={(\frac{1}{v}+{v^{\prime }}^4)}^{1/3}$

18459

16 (b)

$v^{\prime }+u^{2}v=\sin \left(u\right)$

18460

17 (a)

$\sqrt{y^{\prime }+y}={(y^{\prime \prime }+2x)}^{1/4}$

18461

18

$v^{\prime }+\frac{2v}{u}=3$

ID

problem

ODE

18462

4 (a)

$\sin \left(x\right)\cos {\left(y\right)}^2+\cos {\left(x\right)}^2{y}^{\prime }=0$

18463

4 (b)

$y^{\prime }+\sqrt{\frac{1-y^2}{-x^2+1}}=0$

18464

4 (c)

$y-x{y}^{\prime }=b(1+x^2{y}^{\prime })$

18465

5

$x^{\prime }=k(A-nx)(M-mx)$

18466

6

$y^{\prime }=1+\frac{1}{x}-\frac{1}{y^2+2}-\frac{1}{x(y^2+2)}$

ID

problem

ODE

18467

1

$y^2=x(y-x)y^{\prime }$

18468

2

$2x^{2}y+y^3-x^3{y}^{\prime }=0$

18469

3

$2ax+by+(2cy+bx+e)y^{\prime }=g$

18470

4

$\sec {\left(x\right)}^2\tan \left(y\right)y^{\prime }+\sec {\left(y\right)}^2\tan \left(x\right)=0$

18471

5

$y{y}^{\prime }+x=my$

18472

6

$\frac{2x}{y^3}+(\frac{1}{y^2}-\frac{3x^2}{y^4})y^{\prime }=0$

18473

8

$(T+\frac{1}{\sqrt{t^2-T^2}})T^{\prime }=\frac{T}{t\sqrt{t^2-T^2}}-t$

ID

problem

ODE

18474

1

$y^{\prime }+xy=x$

18475

2

$y^{\prime }+\frac{y}{x}=\sin \left(x\right)$

18476

3

$y^{\prime }+\frac{y}{x}=\frac{\sin \left(x\right)}{y^3}$

18477

4

$p^{\prime }=\frac{p+a{t}^3-2p{t}^2}{t(-t^2+1)}$

18478

5

$(T\ln \left(t\right)-1)T=t{T}^{\prime }$

18479

6

$y^{\prime }+\cos \left(x\right)y=\frac{\sin \left(2x\right)}{2}$

18480

7

$y-y^{\prime }\cos \left(x\right)=y^2\cos \left(x\right)(-\sin \left(x\right)+1)$

ID

problem

ODE

18481

2

$x{y^{\prime }}^2+2y^{\prime }-y=0$

18482

3

$2{y^{\prime }}^3+{y^{\prime }}^2-y=0$

18483

4

$y^{\prime }={\mathrm{e}}^{z-y^{\prime }}$

18484

5

$\sqrt{t^2+T}=T^{\prime }$

18485

7

${y^{\prime }}^2(x^2-1)=1$

18486

8

$y^{\prime }={(x+y)}^2$

ID

problem

ODE

18487

1

${\theta }^{\prime \prime }=-p^2\theta$

18488

2 (eq 39)

$\sec {\left(\theta \right)}^2=\frac{m{s}^{\prime }}{k}$

18489

3 (eq 41)

$y^{\prime \prime }=\frac{m\sqrt{1+{y^{\prime }}^2}}{k}$

18490

4 (eq 50)

${\varphi }^{\prime \prime }=\frac{4\pi nc}{\sqrt{v_0^2+\frac{2e(\varphi -V_0)}{m}}}$

18491

8 (eq 68)

$y^{\prime }=x(a{y}^2+b)$

18492

8 (eq 69)

$n^{\prime }=(n^2+1)x$

18493

9 (a)

$v^{\prime }+\frac{2v}{u}=3v$

18494

9 (b)

$\sqrt{-u^2+1}{v}^{\prime }=2u\sqrt{1-v^2}$

18495

9 (c)

$\sqrt{1+v^{\prime }}=\frac{{\mathrm{e}}^u}{2}$

18496

9 (d)

$\frac{y^{\prime }}{x}=y\sin (x^2-1)-\frac{2y}{\sqrt{x}}$

18497

9 (e)

$y^{\prime }=1+\frac{2y}{x-y}$

18498

10 (a)

$v^{\prime }+2uv=2u$

18499

10 (b)

$1+v^2+(u^2+1)v{v}^{\prime }=0$

18500

10 (c)

$u\ln \left(u\right)v^{\prime }+\sin {\left(v\right)}^2=1$

ID

problem

ODE

18501

1 (eq 98)

$4y{y^{\prime }}^3-2x^2{y^{\prime }}^2+4x{y}^{\prime }y+x^3=16y^2$

ID

problem

ODE

18502

1 (eq 100)

${\theta }^{\prime \prime }-p^2\theta =0$

18503

2

$y^{\prime \prime }+y=0$

18504

3

$y^{\prime \prime }+12y=7y^{\prime }$

18505

4

$r^{\prime \prime }-a^{2}r=0$

18506

5

$y^{\prime \prime \prime \prime }-a^{4}y=0$

18507

6

$v^{\prime \prime }-6v^{\prime }+13v={\mathrm{e}}^{-2u}$

18508

7

$y^{\prime \prime }+4y^{\prime }-y=\sin \left(t\right)$

18509

8

$y^{\prime \prime }+3y=\sin \left(x\right)+\frac{\sin \left(3x\right)}{3}$

18510

10

$5x^{\prime }+x=\sin \left(3t\right)$

18511

11

$x^{\prime \prime \prime \prime }-6x^{\prime \prime \prime }+11x^{\prime \prime }-6x^{\prime }={\mathrm{e}}^{-3t}$

18512

14

$x^4{y}^{\prime \prime \prime \prime }+x^3{y}^{\prime \prime \prime }-20x^2{y}^{\prime \prime }+20x{y}^{\prime }=17x^6$

18513

15

$t^4{x}^{\prime \prime \prime \prime }-2t^3{x}^{\prime \prime \prime }-20t^2{x}^{\prime \prime }+12x^{\prime }t+16x=\cos (3\ln \left(t\right))$

ID

problem

ODE

18514

1

$y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y=0$

18515

2

$y^{\prime \prime \prime \prime }-3y^{\prime \prime \prime }+3y^{\prime \prime }-y^{\prime }={\mathrm{e}}^{2x}$

18516

3

$y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y=\cos \left(x\right)$

18517

8

$x^2{y}^{\prime \prime }+3x{y}^{\prime }+y=\frac{1}{x}$